The five points of Calvinism represent the major tenets of Calvinistic thinking. They can be easily remembered by memorizing the acrostic TULIP: Total Depravity, Unconditional Election, Limited Atonement, Irresistible Grace, Perseverance of the Saints.
Total Depravity: This doctrine teaches there is no part of our human nature which has not been affected by the taint of sin. Our intellect, emotions, will, and even physical bodies, have been corrupted by the Fall.
As a point of clarification, total depravity does not mean that humanity is as bad as possible or that no good in any sense can be done by unbelievers (though ultimately any good that does come about should be attributed to God's grace). Rather, it means that in the natural fallen state we are born into we are unable to do any spiritual good that will please God and we cannot come to God by our own strength. This is why some theologians refer to this point, perhaps more accurately, as total inability.
Scripture teaches that in our fallen state we are dead in our trespasses (Eph. 2:1-2) and slaves to sin (John 8:34). Unbelievers are said to be "darkened in their understanding, alienated from the life of God because of the ignorance that is in them, due to their hardness of heart" (Eph. 4:18). Paul says that "those who are in the flesh cannot please God" (Rom. 8:8) and Isaiah states that "all our righteous deeds are like a filthy garment" (Isa. 64:6). This is why Jesus said, "No one can come to me unless the Father who sent me draws him" (John 6:44). (1)
All quotes are from the Battles translation, edited by John T. McNeill. Enjoy!
John Calvin on Spiritual Warfare
JOHN CALVIN ON TOTAL DEPRAVITY
2.1.2 - Man by nature inclines to deluded self-admiration
Here, then, is what God's truth requires us to seek in examining ourselves: it requires the kind of knowledge that will strip us of all confidence in our own ability, deprive us of all occasion for boasting, and lead us to submission...There is, indeed, nothing that man's nature seeks more eagerly than to be flattered...For, since blind self-love is innate in all mortals, they are most freely persuaded that nothing inheres in themselves that deserves to be considered hateful.
Nothing pleases man more than the sort of alluring talk that tickles the pride that itches in his very marrow...But however great such commendation of human excellence is that teaches man to be satisfied with himself, it does nothing but delight in its own sweetness; indeed, it so deceives as to drive those who assent to it into utter ruin...Yet for those confident they can do anything by their own power, things cannot happen otherwise. Whoever, then, heeds such teachers as hold us back with thought only of our good traits will not advance in self-knowledge, but will be plunged into the worst ignorance.
2.1.3 - The two chief problems with self-knowledge
According to carnal judgment, man seems to know himself very well, when, confident in his understanding and uprightness, he becomes bold and urges himself to the duties of virtue, and, declaring war on vices, endeavors to exert himself with all his ardor toward the excellent and the honorable. But he who scrutinizes and examines himself according to the standard of divine judgment finds nothing to lift his heart to self-confidence. And the more deeply he examines himself, the more dejected he becomes, until, utterly deprived of all such assurance, he leaves nothing to himself with which to direct his life aright.
Yet God would not have us forget our original nobility, which he had bestowed upon our father Adam, and which ought truly to arouse in us a zeal for righteousness and goodness...so that sick of our miserable lot we groan, and in groaning we sigh for that lost worthiness. But when we say that man ought to see nothing in himself to cause elation, we mean that he has nothing to rely on to make him proud.
2.1.9 - Sin overturns the whole man
For this reason, I have said that all parts of the soul were possessed by sin after Adam deserted the fountain of righteousness. For not only did a lower appetite seduce him, but unspeakable impiety occupied the very citadel of his mind, and pride penetrated to the depths of his heart...Paul removes all doubt when he teaches that corruption subsists not in one part only, but that none of the soul remains pure or untouched by that mortal disease. For in his discussion of a corrupt nature Paul not only condemns the inordinate impulses of the appetites that are seen, but especially contends the mind is given over to blindness and the heart to depravity.
2.2.10 - The doctrine of free will is always in danger of robbing God of his honor
Nevertheless, what I mentioned at the beginning of this chapter I am compelled here to repeat once more: that whoever is utterly cast down and overwhelmed by the awareness of his calamity, poverty, nakedness, and disgrace has thus advanced farthest in knowledge of himself. For there is no danger of man's depriving himself of too much so long as he learns that in God must be recouped what he himself lacks...If it is the devil's word that exalts man in himself, let us give no place to it unless we want to take advice from our enemy...no one is permitted to receive God's blessings unless he is consumed with the awareness of his own poverty.
2.2.18 - The limits of our understanding
Human reason, therefore, neither approaches, nor strives toward, nor even takes a straight aim at, this truth: to understand who the true God is or what sort of God he wishes to be toward us.
2.2.19 - Man's spiritual blindness shown from John 1:4-5
But we are drunk with the false opinion of our own insight and are thus extremely reluctant to admit that it is utterly blind and stupid in divine matters...Because man's keenness of mind is mere blindness as far as the knowledge of God is concerned...Flesh is not capable of such lofty wisdom as to conceive God and what is God's, unless it be illumined by the Spirit of God.
2.2.20 - Man's knowledge of God is God's own work
This doubtless means man's mind can become spiritually wise only in so far as God illumines it.
Christ also confirmed this most clearly in his own words when he said: "No one can come to me unless it be granted by my Father" [John 6:44 p.]...But nothing is accomplished by preaching him if the Spirit, as our inner teacher, does not show our minds the way. Only those men, therefore, who have heard and have been taught by the Father come to him.
It therefore remains for us to understand that the way to the Kingdom of God is open only to him whose mind has been made new by the illumination of the Holy Spirit. Paul, however, having expressly entered this discussion, speaks more clearly than all [I Cor. 1:18 ff.]. After condemning the stupidity and vanity of all human wisdom and utterly reducing it to nothing [cf. I Cor. 1:13 ff.], he concludes: "The natural man cannot receive the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned" [I Cor. 2:14]. Whom does he call "natural"? The man who depends upon the light of nature. He, I say, comprehends nothing of God's spiritual mysteries. Why is this? Is it because he neglects them out of laziness? No, even though he try, he can do nothing, for "they are spiritually discerned." What does this mean? Because these mysteries are deeply hidden from human insight, they are disclosed solely by the revelation of the Spirit. Hence, where the Spirit of God does not illumine them, they are considered folly.
2.2.21 - Without the light of the Spirit, all is darkness
If we confess that we lack what we seek of God, and he by promising it proves our lack of it, no one should now hesitate to confess that he is able to understand God's mysteries only in so far as he is illumined by God's grace. He who attributes any more understanding to himself is all the more blind because he does not recognize his own blindness.
2.2.26 - The natural instinct that treats the "good" and the "acceptable" alike has nothing to do with freedom
To sum up, much as a man desires to follow what is good, still he does not follow it. There is no man to whom eternal blessedness is not pleasing, yet no man aspires to it except by the impulsion of the Holy Spirit.
2.2.27 - Our will cannot long for the good without the Holy Spirit
We are all sinners by nature; therefore we are held under the yoke of sin.
Confess that you have all these things from God: whatever good you have is from him; whatever evil, from yourself...Nothing is ours but sin.
2.3.2 - Romans, ch. 3, as witness for man's corruption
Now his intention in this passage is not simply to rebuke men that they may repent, but rather to teach them that they have all been overwhelmed by an unavoidable calamity from which only God's mercy can deliver them.
Let this then be agreed: that men are as they are here described not merely by the defect of depraved custom, but also by depravity of nature. The reasoning of the apostle cannot otherwise stand: Except out of the Lord's mercy there is no salvation for man, for in himself he is lost and forsaken [Rom. 3:23 ff.]...it is futile to seek anything good in our nature.
2.3.5 - Man sins of necessity, but without compulsion
Because of the bondage of sin by which the will is held bound, it cannot move toward good, much less apply itself thereto; for a movement of this sort is the beginning of conversion to God, which in Scripture is ascribed entirely to God's grace...Therefore simply to will is of man; to will ill, of a corrupt nature; to will well, of grace.
2.3.6 - Men's inability to do good manifests itself above all in the work of redemption, which God does quite alone
God begins his good work in us, therefore, by arousing love and desire and zeal for righteousness in our hearts; or, to speak more correctly, by bending, forming, and directing, our hearts to righteousness. He completes his work, moreover, by confirming us to perseverance.
I also say that it is created anew; not meaning that the will now begins to exist, but that it is changed from an evil to a good will...everything good in the will is the work of grace alone.
2.3.8 - Scripture imputes to God all that is for our benefit
Surely there is ready and sufficient reason to believe that good takes its origin from God alone. And only in the elect does one find a will inclined to good.
But since the whole of Scripture proclaims that faith is a free gift of God, it follows that when we, who are by nature inclined to evil with our whole heart, begin to will good, we do so out of mere grace...For it always follows that nothing good can arise out of our will until it has been reformed; and after its reformation, in so far as it is good, it is so from God, not from ourselves.
2.3.10 - God's activity does not produce a possibility that we can exhaust, but an actuality to which we cannot aid
Men indeed ought to be taught that God's loving-kindness is set forth to all who seek it, without exception. But since it is those on whom heavenly grace has breathed who at length begin to seek after it, they should not claim for themselves the slightest part of his praise. It is obviously the privilege of the elect that, regenerated through the Spirit of God, they are moved and governed by his leading.
I have come, you say, of my own free choice; I have come of my own will. Why are you so puffed up? Do you wish to know that this also has been given you? Hear Him calling, "No one comes to me unless the Father draws him." [John 6:44 p.].
(1) See Wayne Grudem, Systematic Theology, pgs. 497-498