(note to those who read this: I'm not a calvinist, I'm not even fond of calvinism, it's just something I studied last year... just Noding what I know, not necessarily what I like :-) )

This is the intro I wrote in a (not-so) small paper on Calvinism last year for ENGL1302 (Argumentative Writing):
"In the first protestant reformation, many theologians sought to ‘purify’ Catholicism, the church of the day. John Calvin was one of these. His teachings not only reformed the beliefs of his followers and contemporaries, but also form the basis of many modern protestant faiths. The crux of his doctrine is predestination. The tenets of those who follow the teachings of Calvin can easily be remembered by the acronym ‘T.U.L.I.P.’. These tenets include total hereditary depravity, unconditional election, limited atonement, irresistible grace, and perseverance of the saints."
ok.. to explain these...

Total Hereditary Depraviy

This doctrine teaches that man, in and of himself, is utterly incapable of pleasing God in any way. This is usually taken from Ephesians 4:18. The value of this doctrine, however, depends on how you define the word 'good'... From a secular standpoint, this doctrine holds little value, as society can (and historically will) change his/their definition of what's 'good'. The doctrine only works if you define 'good' by God's standards(meaning to follow God wholeheartedly and to keep his commands ('Love the Lord your God with all your heart, mind, soul, and strength' and 'Love your neighbor as yourself', among others.)

Unconditional Election

This doctrine teaches that men are called untosalvation, and that they do nothing to merit such a call. This is usually taken from Romans 9:11. This is the part that terrified people into trusting Calvin, it made them constantly question their election (see predestination, foreknowledge). hmmm. Makes you want to hear fom a calvinist who thinks he/she's predestined to go to hell!

Limited Atonement

This doctrine teaches that Christ's atoning blood counts only for those who were/are/will be elected unto salvation. I've searched the scriptures, and conversed with calvinists, and it seems that this point has little to no scriptural backing... in fact, I can think of two right off the top of my head that refute it (Romans 3:23, and Isaiah 52:5-6.) This doctrine is also reffered to in some circles as "Doctrines of the Elect".

Irresistable Grace

This doctrine teaches that once God elects you, poof! you're elected! There's nothing you can do about it. Once again, the only backing I've ever seen for this point has been references to other calvinists who believe it (and not scripture itself). On the surface, it seems logical enough, but when you apply a little xenoic philosophy (divisi ad ridiculo)to it, it crumbles... this is because it forgets to include free will, which God certainly has granted man (or else, how would Jonah have been able to flee to Tarshish?)

Perseverance of the Saints

This doctrine teaches that once someone is saved, they can't do anything to lose it (aka: "once saved, always saved"). Those that support this doctrine quote 1 John 1:9. Those who don't quote Matthew 12:31. Taken in context, though, the latter quote is discovered not to apply to Christians, as Christ was speaking to Pharisees, who saw him, in his glory, and not only denied his divinity to his face, but went so far as to call him Beelzebub. (this is often referred to as "the unpardonable sin"... Christians can't commit this because, frankly, the only evidence we have of Christ is through (remarkably accurate) historical documents, and personal faith, not face-to-face contact, so any denial we could make of Christ would amount to more a denial of faith than a denial of divinity.

The effects of calvinism can still be seen today in modern churches (mostly Baptist, Presbyterian, and a few other Protestant faiths.) Nowadays, however, many churches choose to teach only the tenets of Calvinism that they agree with (usually the first and last points). The middle three have been all but abandoned in mainstream Christianity, and in some instances have been labeled 'blasphemous'.

For some interesting calvinist reading, see the Westminster Confession of Faith. It was heavily influenced by the teachings of Calvin.

I hope these few simple definitions and apologetics help anyone studying the issue...