It's quite easy. There is an acrostic, TULIP, that sums up the major points of Calvinism:
T - Total Depravity. Humans are unable to turn to God on their own, and are unable even to perform any good works at all. See Romans 3:10-18
There is no one who is righteous, not even one; there is no one who has understanding, there is no one who seeks God. All have turned aside, together they have become worthless; there is no one who shows kindness, there is not even one. Their throats are opened graves; they use their tongues to deceive. The venom of vipers is under their lips. Their mouths are full of cursing and bitterness. Their feet are swift to shed blood; ruin and misery are in their paths, and the way of peace they have not known. There is no fear of God before their eyes.
U - Unconditional Election. God chooses those whom he desires to save. This election is without regard to the merit of the individual so chosen. The converse is that God chooses some to be eternally damned, again without regard to the merit of the individual.
L - Limited Atonement. Christ died only for the sins of those he has unconditionally elected.
I - Irresistible Grace. If you are among those chosen to be saved, God's grace is irresistible and you will come to a knowledge of God. In other words, God is like the Borg, "Resistance is futile. You will be assimilated!"
P - Perseverance of the saints. Once you are saved you cannot lose salvation. Interestingly, this doctrine also embraces the idea of a life-long sanctification process.
One of my professors, a Baptist, summed it up as:
T = We're scum.
U = God chooses which scum goes to heaven and which to hell.
L = Jesus died only for the heaven-bound scum.
I = God doesn't give the heaven-bound scum a choice in the matter.
P = Nor does he allow scumminess to interfere with the process.
This makes a bit from Gilbert and Sullivan's Patience to run through my mind:
Take of these elements all that is fusible,
Melt them all down in a pipkin or crucible,
Set them to simmer and take off the scum
And a Heavy Dragoon is the residuum!