Calvinists indeed believe they can only make educated guesses about others; if someone you thought was saved falls away, the conclusion is they were never actually saved. But Calvinism teaches that "infallible assurance of faith" is available to believers about themselves.

The Grounds of Assurance

The Westminster Confession of Faith says in chapter 18:

This certainty is not a bare conjectural and probable persuasion grounded upon a fallible hope; but an infallible assurance of faith founded upon the divine truth of the promises of salvation, the inward evidence of those graces unto which these promises are made, the testimony of the Spirit of adoption witnessing with our spirits that we are the children of God, which Spirit is the earnest of our inheritance, whereby we are sealed to the day of redemption.

Similarly, the Belgic Confession says in article 24:

So we would always be in doubt, tossed back and forth without any certainty, and our poor consciences would be tormented constantly if they did not rest on the merit of the suffering and death of our Savior.

And the Canons of Dort say in articles 12 and 13 of section 1:

Assurance of their eternal and unchangeable election to salvation is given to the chosen in due time, though by various stages and in differing measure. Such assurance comes not by inquisitive searching into the hidden and deep things of God, but by noticing within themselves, with spiritual joy and holy delight, the unmistakable fruits of election pointed out in God’s Word—such as a true faith in Christ, a childlike fear of God, a godly sorrow for their sins, a hunger and thirst for righteousness, and so on.

In their awareness and assurance of this election, God’s children daily find greater cause to humble themselves before God, to adore the fathomless depth of God’s mercies, to cleanse themselves, and to give fervent love in return to the One who first so greatly loved them. This is far from saying that this teaching concerning election, and reflection upon it, make God’s children lax in observing his commandments or carnally self-assured. By God’s just judgment this does usually happen to those who casually take for granted the grace of election or engage in idle and brazen talk about it but are unwilling to walk in the ways of the chosen.

So we see several sources of assurance:

• Westminster points to "the divine truth of the promises of salvation," and the Belgic Confession specifies "the merit of the suffering and death of our Savior" upon which those promises rest. Westminster cites these Scriptures for support:

Hebrews 6:11 But we passionately want each of you to demonstrate the same eagerness for the fulfillment of your hope until the end. 17 In the same way God wanted to demonstrate more clearly to the heirs of the promise that his purpose was unchangeable, and so he intervened with an oath, 18 so that we who have found refuge in him may find strong encouragement to hold fast to the hope set before us through two unchangeable things, since it is impossible for God to lie. 19 We have this hope as an anchor for the soul, sure and steadfast, which reaches inside behind the curtain

• Westminster continues, "the inward evidence of those graces unto which these promises are made," specified by Dort as "a true faith in Christ, a childlike fear of God, a godly sorrow for their sins, a hunger and thirst for righteousness, and so on," and Westminster cites:

2 Peter 1:4 Through these things he has bestowed on us his precious and most magnificent promises, so that by means of what was promised you may become partakers of the divine nature, after escaping the worldly corruption that is produced by evil desire. 5 For this very reason, make every effort to add to your faith excellence, to excellence, knowledge. 10 Therefore, brothers and sisters, make every effort to be sure of your calling and election. For by doing this you will never stumble into sin. 11 For thus an entrance into the eternal kingdom of our Lord and Savior, Jesus Christ, will be richly provided for you.

1 John 2:3 Now by this we know that we have come to know God: if we keep his commandments.

1 John 3:14 We know that we have crossed over from death to life because we love our fellow Christians. The one who does not love remains in death.

2 Corinthians 1:12 For our reason for confidence is this: the testimony of our conscience, that with pure motives and sincerity which are from God—not by human wisdom but by the grace of God—we conducted ourselves in the world, and all the more toward you.

• Westminster wraps it up with, "The testimony of the Spirit of adoption witnessing with our spirits that we are the children of God," referring to Romans 8:15-16, "which Spirit is the earnest of our inheritance, whereby we are sealed to the day of redemption," citing these verses:

Ephesians 1:13 And when you heard the word of truth (the gospel of your salvation)—when you believed in Christ—you were marked with the seal of the promised Holy Spirit, 14 who is the down payment of our inheritance, until the redemption of God’s own possession, to the praise of his glory.

Ephesians 4:30 And do not grieve the Holy Spirit of God, by whom you were sealed for the day of redemption.

2 Corinthians 1:21 But it is God who establishes us together with you in Christ and who anointed us, 22 who also sealed us and gave us the Spirit in our hearts as a down payment.

Unstable Grounds of Assurance

Unfortunately, people often seek means of assurance that will fail them. One way is by searching deeply into the hidden things of God. Another is by looking primarily to yourself, rather than to Christ.

As you'll recall, the Canons of Dort said, "Assurance comes not by inquisitive searching into the hidden and deep things of God." Many people agonize, "Is my name in the book of life? Did God's decree include me? Am I elect?" In so agonizing, they may never reach any kind of assurance, because they are looking in the wrong place. The Bible and the reformed confessions teach that the "hidden things belong to God" (Deuteronomy 29:29). Theologians of every era caution that believers shouldn't inquire too deeply into God's hidden will, but into his revealed will. God has given promises and he has revealed means of "making your calling sure." He has not given us a copy of the book of life, for us to inquire directly into whether our name or our un-evangelized neighbor's name is there. He's made it more complicated for us by requiring a life of discipleship.

Another false means of assurance is trying to "prove" oneself to God (or to oneself). This slavish adherence to the regulations of Scripture does not produce assurance, but "constantly" torments the conscience, as the Belgic Confession says. Instead, we must put our trust in the only one who could fulfill the law, Jesus Christ. Obviously, the Westminster Confession does say we should look for fruit in ourselves, but Robert Murray M'Cheyne gives a good rule of thumb for avoiding the trap of introspection: "For every look at yourself, take ten looks at Christ."

Another false means of assurance is a fruit of so-called "decision theology" popularized by Charles Finney. It's similar to the previous one mentioned in that it rests in subjectivity. Many people look to the sincerity of their initial confession when they responded to an altar call or prayed a prayer. Such people may end up praying over and over, or responding to countless altar calls, never coming to true assurance of faith. This is because we ourselves are finicky. Again, the true means of assurance come from looking to the one who is alone faithful (and always sincere). Tim Challies says:

When you seek assurance of your salvation, where do you look? Will you take refuge in the sincerity of your prayer? Will you comfort yourself by saying, “I meant it with all my heart”? If you take refuge in your own sincerity or in the passion you felt years ago when you prayed a prayer, you are building your assurance on shakey ground.

The Non-Necessity of Assurance

After establishing the grounds of assurance, the Westminster Confession goes on to say:

This infallible assurance does not so belong to the essence of faith, but that a true believer may wait long, and conflict with many difficulties, before he be partaker of it: yet, being enabled by the Spirit to know the things which are freely given him of God, he may, without extraordinary revelation in the right use of ordinary means, attain thereunto. And therefore it is the duty of every one to give all diligence to make his calling and election sure, that thereby his heart may be enlarged in peace and joy in the Holy Ghost, in love and thankfulness to God, and in strength and cheerfulness in the duties of obedience, the proper fruits of this assurance; so far is it from inclining men to looseness.

In other words, true believers may not have assurance of salvation immediately, and that's okay, just as Dort said: "Assurance of their eternal and unchangeable election to salvation is given to the chosen in due time, though by various stages and in differing measure." But they ought to strive toward it in order to be more joyful in the Holy Spirit and thankful to God. Westminster continues by saying that believers may even lose their assurance but that it's always possible to regain:

True believers may have the assurance of their salvation divers ways shaken, diminished, and intermitted; as, by negligence in preserving of it, by falling into some special sin which wounds the conscience and grieves the Spirit; by some sudden or vehement temptation, by God's withdrawing the light of His countenance, and suffering even such as fear Him to walk in darkness and to have no light: yet are they never so utterly destitute of that seed of God, and life of faith, that love of Christ and the brethren, that sincerity of heart, and conscience of duty, out of which, by the operation of the Spirit, this assurance may, in due time, be revived; and by the which, in the mean time, they are supported from utter despair.

Distinguishing True Assurance from False

The Canons of Dort say that "by God's just judgment" some "who casually take for granted the grace of election or engage in idle and brazen talk about it but are unwilling to walk in the ways of the chosen" become "carnally self-assured" rather than having an actual assurance of faith. So how can an "infallible assurance" (in Westminster's language) and this "carnal self-assurance" be distinguished?

A.A. Hodge's commentary on the Westminster Confession takes a stab at the question.

True assurance, however, may be distinguished from that which is false by the following tests:

1. True assurance begets unfeigned humility; false assurance begets spiritual pride. 1 Corinthians 15:10; Galatians 6:14.

2. The true leads to increased diligence in the practice of holiness; the false leads to sloth and self-indulgence. Psalm 51:12-13,19.

3. The true leads to candid self-examination and to a desire to be searched and corrected by God; the false leads to a disposition to be satisfied with appearance and to avoid accurate investigation. Psalm 139:23-24.

4. The true leads to constant aspirations after more intimate fellowship with God. 1 John 3:2-3.

It is common for Calvinists to cite 1 John 2:19 in the case of those who either were falsely assured or who deceived others (knowingly or not) into believing they were saved:

They went out from us, but they did not really belong to us, because if they had belonged to us, they would have remained with us. But they went out from us to demonstrate that all of them do not belong to us.

Conclusion

Calvinists teach that to be assured of salvation, you must look first to Christ, his merits, and his promises, then to the fruits of faith that he has granted you. It is not found by inquiring into the decree of election, nor by looking chiefly to yourself. It is not necessary to be assured of salvation in order to be saved, but it is a good thing to strive for nonetheless. There are ways of distinguishing it from "carnal self-assurance," and those who have such false assurance are mistaken about their salvation.

John MacArthur, a five-pointer, wrote a whole book about this. From what I remember, it's entirely consistent with the confessions. Also consistent with the confessions: Calvin's views.