I. Although the light of nature, and the works of creation and providence do so far manifest the goodness, wisdom, and power of God, as to leave men unexcusable; yet are they not sufficient to give that knowledge of God, and of His will, which is necessary unto salvation. Therefore it pleased the Lord, at sundry times, and in divers manners, to reveal Himself, and to declare that His will unto His Church; and afterwards for the better preserving and propagating of the truth, and for the more sure establishment and comfort of the Church against the corruption of the flesh, and the malice of Satan and of the world, to commit the same wholly unto writing; which makes the Holy Scripture to be most necessary; those former ways of God's revealing His will unto His people being now ceased.Yet there is apparently doubt in the minds of some that this confession is explicitly cessationist with respect to the revelatory gifts. While the text itself is rather clear on its face, it may be worth considering what Reformed commentators have said in their commentaries on the Confession or related catechisms.
 ROM 2:14 For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves: 15 Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another; 1:19 Because that which may be known of God is manifest in them; for God hath shewed it unto them. 20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse. PSA 19:1 The heavens declare the glory of God; and the firmament sheweth his handiwork. 2 Day unto day uttereth speech, and night unto night sheweth knowledge. 3 There is no speech nor language, where their voice is not heard. ROM 1:32 Who knowing the judgment of God, that they which commit such things are worthy of death, not only do the same, but have pleasure in them that do them. 2:1 Therefore thou art inexcusable, O man, whosoever thou art that judgest: for wherein thou judgest another, thou condemnest thyself; for thou that judgest doest the same things.
 1CO 1:21 For after that in the wisdom of God the world by wisdom knew not God, it pleased God by the foolishness of preaching to save them that believe. 2:13 Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual. 14 But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
 HEB 1:1 God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets.
 PRO 22:19 That thy trust may be in the Lord, I have made known to thee this day, even to thee. 20 Have not I written to thee excellent things in counsels and knowledge, 21 That I might make thee know the certainty of the words of truth; that thou mightest answer the words of truth to them that send unto thee? LUK 1:3 It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus, 4 That thou mightest know the certainty of those things, wherein thou hast been instructed. ROM 15:4 For whatsoever things were written aforetime were written for our learning, that we through patience and comfort of the scriptures might have hope. MAT 4:4 But he answered and said, It is written, Man shall not live by bread alone, but by every word that proceedeth out of the mouth of God. 7 Jesus said unto him, It is written again, Thou shalt not tempt the Lord thy God. 10 Then saith Jesus unto him, Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve. ISA 8:19 And when they shall say unto you, Seek unto them that have familiar spirits, and unto wizards that peep, and that mutter: should not a people seek unto their God? for the living to the dead? 20 To the law and to the testimony: if they speak not according to this word, it is because there is no light in them.
 2TI 3:15 And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. 2PE 1:19 We have also a more sure word of prophecy; whereunto ye do well that ye take heed, as unto a light that shineth in a dark place, until the day dawn, and the day star arise in your hearts.
 HEB 1:1 God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets, 2 Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds.
It will be noted that the Confession sharply contradicts the view popularized today by the neo-Pentecostal movement. In essence this view would have us believe that we can have the same charismatic gifts today-- such as prophecy, speaking in tongues, and healing -- that we read occurred in the age of the apostles. This is a very serious error. In essence it is a result of a failure to grasp the biblical teaching concerning the history of salvation. The Bible itself makes it clear that there are many things in the history of redemption that cannot, and will not, be repeated. There will never again by a universal flood, or a crossing of the Red Sea, or a virgin birth. Never again will there be an outpouring of the Holy Spirit such as took place on the day of Pentecost. The sending of the Holy Spirit is just as much an unrepeatable event as the birth of Christ was. It is for this reason that the miracles -- the signs and wonders -- that we read of in the Bible were not constantly occurring but, rather, centered on the major events in the process of revelation. Note, for instance, how few the miracles are in the Bible until we come to the time of Moses (the author of the first part of the Bible). Note also how the signs and wonders that we read of in the book of Acts are always associated with the presence of the apostles. For these, and similar facts, there is a reason. The reason is that these signs and wonders were given by God to attest and confirm that these men were his spokesmen. And since this process came to completion in the finished work of Christ, and the testimony of these men is now deposited in the Scriptures, the Bible alone is God's present revelation.G. I. Williamson, The Westminster Confession of Faith: For Study Classes, pp. 4-5 (link)
Quest. III. "Are these former Ways of God's revealing his Will unto his People now ceased?"
Well then, do not the Enthusiasts and Quakers err, who maintain, That the Lord hath not ceased yet to reveal his Will as he did of old?
By what Reasons are they confuted?
1st, Because God who at sundry Times, and in divers Manners, spake in Times past unto the Fathers by the Prophets, hat in these last Days spoken unto us by his Son. Heb. 1:1-2. The Apostle calls the Time of the New Testament the last Days, because under the same, there is no more Alteration to be expected, but all Things are to abide without adding, or taking away, as was taught and ordained by Christ, until the last Day; See also Joel 2:18, Acts 2:17. The Ways and Manners of old were first by Inspiration, 1 Chron. 15:1, Isai. 49:21, 2 Pet. 1:21. Secondly, By Visions, Num. 12:6,8. Thirdly, By Dreams, Job 33:14,15, Gen. 40:8. Fourthly, By Urim and Thummim, Num. 27:21, 1 Sam. 30:7,8. Fifthly, By Signs, Gen. 32:24, Exod. 13:21. Sixthly, By Audible Voice, Exod. 20:1, Gen. 22:15. All which do end in Writing, Exod. 17:17, 14 which is a most sure and infallible Way of the Lord's revealing his Will unto his People.
David Dickinson, Truth's Victory over Error (a commentary on the WCF), pp. 31-32 (link)
Q. 26. Why are the scriptures from Matthew to the end of the Revelation, called the New Testament?Fisher's Catechism (The Shorter Catechism Explained) at Question 2 (link)
A. Because they contain the most clear and full revelation, and actual ratification of the covenant of promise, by the death of Christ the Testator, who is also the living Executor of his own testament, Rev. 1:18 -- "I am he that liveth and was dead; and behold, I am alive for evermore." John 14:19 -- "Because I live, ye shall live also."
Q. 27. Will this New Testament dispensation of the grace of God ever undergo any other alteration?
A. No; it will remain new and unalterable, till the second coming of the Lord Jesus, Mat. 26:29.
Q. 46. Is the light within men, or the Spirit without the word, which is pretended to by the Quakers, and other enthusiasts, to be used as any rule for our direction?
A. No; because whatever light or spirit is pretended to, without the word, it is but darkness, delusion, and a spirit of error, 1 John 4:1, 6.
Q. Why doth not God still work miracles for the confirmation of the scriptures? A. Because they were only necessary to establish truth at first, and to awaken the world to consider and receiver it; and if always wrought, be esteemed common things, and make no impression on the minds of men, Exod. iv.--xiv. &c.John Brown, "An Essay Towards and Easy, Plain, Practical, and Extensive Explication of the Assembly's Shorter Catechism" (link)
The idea of the completeness of Scripture also implies that nothing is to be added to or taken from them at any time. The canon of Scripture is complete and closed, and all that men need for faith and life is therein contained. Hence no supposed new revelations of the Spirit are to be added, and the opinions and traditions of men are to be excluded.Francis Robert Beattie, The Presbyterian Standards, p. 49 (link)
These are "the ONLY rule to direct us." We have seen that they are a rule, but now we see there is none other.William Paton Mackay, Notes on the Shorter Catechism, pp. 5-6 (link)
The fourth proposition asserts, that this revelation has been committed to writing until the time of Moses, or for a period of two thousand five hundred years, no part of the sacred books was written. God then communicated his will to the Church by immediate revelation; and the long lives of the patriarchs enabled them to preserve uncorrupted what was so revealed, and to transmit it from generation to generation. Two persons might have conveyed it down from Adam to Abraham; for Methuselah lived above three hundred years while Adam was yet alive, and Shem lived almost a hundred years with Methuselah, and above a hundred years with Abraham. But after the lives of men severe shortened, and revelation was greatly enlarged, it pleased God that the whole of his revealed will should be committed to writing, that the Church might have a standing rule of faith and practice, by which all doctrines might be examined, and all actions regulated,–that sacred truth might be preserved uncorrupted and entire,–that it might be propagated throughout the several nations of the earth, and might be conveyed down to all succeeding generation. Though, in the infancy of the Church, God taught his people without the written Word, yet now that he former ways of revealing his will to his people have ceased, the Holy Scripture, or written Word, is most necessary. Without this the Church would be left to the uncertainty of tradition and oral teaching; but the written Word is a sure test of doctrines, and a light in a dark place, both of which are most necessary.–Isa viii. 20; 2 Pet. i. 19.Robert Shaw, The Reformed Faith: An Exposition of the Westminster Confession of Faith
Hence, the Confession teaches in this section --A.A. Hodge, The Westminster Confession: A Commentary
3. That consequently it has pleased God, of his sovereign grace, to make, in various ways and at different times, a super natural revelation of himself and of his purposes to a chosen portion of the human family. And that --
4. God has been pleased subsequently to commit that revelation to writing, and it is now exclusively embraced in the Sacred Scriptures.
Since, as above shown, the light of nature is insufficient to enable men to attain such a knowledge of God and his will as is necessary for salvation, it follows -- (1.) That a supernatural revelation is absolutely necessary for man; and, (2.) From what natural religion alone teaches us of the character of God, it follows that the giving of such a revelation is in the highest degree antecedently probable on his part. Man is essentially a moral agent, and needs a clearly revealed rule of duty; and a religious being, craving communion with God. In his natural state these are both unsatisfied. But God is the author of human nature. His intelligence leads us to believe that he will complete all his works and crown a religious nature with the gift of a religion practically adequate to its wants. The benevolence of God leads us to anticipate that he will not leave his creatures in bewilderment and ruin for the want of light as to their condition and duties. And his righteousness occasions the presumption that he will at some time speak in definite and authoritative tones to the conscience of his subjects. (3.) As a matter of fact, God has given such a revelation. Indeed he has in no period of human history left himself without a witness. His communications to mankind through the first three thousand years were made in very "diverse manners"-- by theophanies and audible voices, dreams, visions, the Urim and Thummim, and prophetic inspiration; and the results of these communications were diffused and perpetuated by means of tradition.
As miracles are now ceased, so such a method of confirming divine revelation is not necessary in all succeeding ages: God did not design to make that dispensation too common, nor to continue the evidence it affords, when there was no necessity thereof.Thomas Ridgeley, A Body of Divinity, p. 115
BONUS (on the topic, but not directly addressing what the standards say):
2. After the faith of Christ was sufficiently confirmed, miracles ceased; and it was fit they should cease, for God doth nothing unnecessarily. The Christian doctrine is the same that it was, and is to be the same till the end of the world; we have a sure and authentic record of it, which is the holy scriptures. The truth of Christ's office and doctrine is fully proved, and cometh transmitted to us by the consent of many successions of ages, in whose experience God hath blessed it to the converting, comforting, and saving of many a soul. Look, as the Jews, every time the law was brought forth, were not to expect the thunderings and lightnings, and the voice of the terrible trumpet, with which it was given at first on Mount Sinai (one solemn confirmation served for after ages); they knew it was a law given by the ministry of angels, and so entertained it with veneration and respect; so Christianity needed to be once solemnly confirmed (after ages have the use of the first miracles); for the apostle compareth these two things, the giving of the law and the gospel: Heb. 2:2-4, 'For if the word spoken by angels was stedfast, and every transgression and disobedience received a just recompense of reward: how shall we escape if we neglect so great salvation, which at first began to be spoken by the Lord, and was confirmed to us by them that heard him?' we must be contented with God's owning it now only in the way of his Spirit and providence.Thomas Manton, Seventh Sermon on 2 Thessalonians, Chapter 2, (link)