Any systematic understanding of the Bible, which is what "Calvinism" is, cannot be reduced to just a few sound-bite bullet points. Many who don't understand the first thing about the theology they deprecate want to do this. It's understandable, in a way. I mean, they despise something, so they don't want to spend a lot of time understanding it. (Pastors should be called to higher requirements, of course.)
So, I thought it might be useful to summarize what the 5 points of Calvinism really mean in a sound bite format, as well as a (very!) slightly more in-depth description of each. Anybody who is against Calvinism should at least understand what it really teaches, not what their traditions and intuitions tell them it teaches.
Sound bite: We really truly are dead in our sins and trespasses.
Slightly more information: Sin pervades every part of our lives. It does not erase anything in our nature, but it weighs us down. This is clearly true of our physical bodies (we get sick and die) and mental facilities (we are limited in our understanding and our "foolish hearts are darkened"); so why should this not be true of our wills also?
Sound bite: God loved me enough to save me in spite of the fact that I hated Him.
Slightly more information: God did not wait for me to choose Him, because (due to Total Depravity) I never would have chosen Him on my own. He chose me not because I was better, not because I was smarter or more spiritually sensitive: just because He loves me. Otherwise, I could take at least some credit for "accepting Jesus" - sure,
maybe God did 99%, but my 1% would still be the deciding factor.
Sound bite: Jesus's death actually saved me.
Slightly more information: Jesus's death on the cross didn't just make me morally neutral so I could make the choice on my own. It didn't just make me savable, my salvation waiting for my own good will to activate. Rather, it actually saved me - Jesus's sacrifice really did pay my sin debt and save me from the hell I deserve.
Sound bite: God loved me enough to save me in spite of the fact that I would have rejected Him.
Slightly more information: Our depravity really does hold down our will. It's not that we don't have free will. It may surprise you, but Calvinists believe that we DO have free will. The problem, as Jonathan Edwards wrote, is that our will can freely choose only from the options that our nature presents to it. Sadly, the natural man's nature (short of God's grace) presents only evil options. Even when we do things that seem on the surface pleasing to God (helping somebody), there are always sinful motives involved. And ultimately, God's common grace is what supplies those better motives, so that all the glory goes to Him.
Perseverance of the Saints
Sound bite: God keeps me safe even though at times I want to run from Him
Slightly more information: God doesn't just save me initially: He keeps me saved in spite of myself. When God saves us, we are spiritually reborn (2 Cor 5:17). This does not mean God removes our sin nature immediately - that will happen when we are glorified. We are saved from the penalty due to us for that sin. But, just as man kept his animal nature when given a spiritual nature, we keep our sin nature even when we are saved from it. If God didn't keep me safe, again I could take credit: sure, God, you saved me originally, but I was the one who kept myself saved.
A final note: My Arminian Christian friends may be objecting right now. "No Christian would ever say they even get 0.001% credit for their own salvation." That's totally true. But that's what I believe their tradition logically requires. Now, I am glad for my Arminian friends' inconsistency on this point. I've noticed that when they talk about their own salvation, they are effectively Calvinists: they always talk as if God did everything. It's only when they start talking philosophically, talking about what God theoretically does to other (unnamed) people, that they start straying into Arminian directions. It's like the old saying: even a metaphysical solipsist looks both ways before crossing the street.