The short and sweet: All humans are inherently sinful by nature, from the earliest moment of their creation. This depravity assures the following: man is not incapable of doing good, but he is incapable of not doing evil.
The Biblical basis:
Isaiah 64:6 All of our righteous deeds are like filthy rags in the sight of God.
Matthew 7:17-18 Every good tree bears good fruit, but every corrupt tree bears evil fruit. A good tree cannot bear bad fruit, and a bad tree cannot bear good fruit.
Jeremiah 17:9 The heart is deceitful above all things, and desperately wicked.
Psalm 58:3 The wicked are estranged from the womb; they go astray from birth.
Ephesians 2:1, Ephesians 2:5 Man is dead in his trespasses and sins.
Romans 3;10-11 As it is written, "there is none righteous, no not one. There are none who seek after God."
Romans 8:7 The mind that is set on the flesh is hostile to God. It does not submit itself to God, because it cannot.
The common sense: All that is needed is for a person to live a little while in this world for them to encounter irrefutable evidence before their very eyes that all of humanity, individually, is horrendously and inescapably internally corrupt. Good people don't do bad things. Everybody does bad things. Therefore nobody is a good person. It is self-evident. The only way to avoid the conclusion that we are not good is by rationalizing that "bad" things are not really "bad." No one in their right noggin can deny that these "good people" do bad things, but to hold on to the hope that we are good (only necessary if you believe that people must earn heaven by being good), the evil that we do must be minimized. It gets explained away as merely being 'imperfections,' 'flaws,' 'mistakes,' etc. But in doing this, we deny the existence of sin, and that denies the motive for Christ to have gone to the Cross. What would be the point of dying for the sins of mankind if mankind could redeem itself by being good? Ignoring the blatantly obvious depravity of man is to declare that Jesus died in vain.
PS the only reason man can do any good at all is by the grace of God that enables him to. So a more forceful presentation of total depravity would hold that man is incapable of doing any good by his own efforts, which is utterly true as well.
The short and sweet: God chooses who will be saved. They do not attain salvation themselves. It is God who initiates and man who responds, not the other way around. Salvation is therefore a free gift and no one can say that they deserved it, or that they accomplished it through some effort or desire on their part.
The Biblical basis:
Ephesians 1:4-5 "He chose us in Him before the foundation of the world, that we should be holy and without blame before Him in love, 5 having predestined us to adoption as sons by Jesus Christ to Himself, according to the good pleasure of His will, "
Romans 9:15-17 "15 For He says to Moses, “I will have mercy on whomever I will have mercy, and I will have compassion on whomever I will have compassion.” 16 So then it is not of him who wills, nor of him who runs, but of God who shows mercy."
The common sense: Then, in the fulness of time, He purchased me with His blood; He let His heart run out in one deep gaping wound for me long ere I loved Him. Yea, when He first came to me, did I not spurn Him? When He knocked at the door, and asked for entrance, did I not drive Him away, and do despite to His grace? Ah, I can remember that I full often did so until, at last, by the power of His effectual grace, He said, "I must, I will come in;" and then He turned my heart, and made me love Him. But even till now I should have resisted Him, had it not been for His grace. Well, then since He purchased me when I was dead in sins, does it not follow, as a consequence necessary and logical, that He must have loved me first? Did my Saviour die for me because I believed on Him? No; I was not then in existence; I had then no being. Could the Saviour, therefore, have died because I had faith, when I myself was not yet born? Could that have been possible? Could that have been the origin of the Saviour's love towards me? Oh! no; my Saviour died for me long before I believed. "But," says someone, "He foresaw that you would have faith; and, therefore, He loved you." What did He foresee about my faith? Did He foresee that I should get that faith myself, and that I should believe on Him of myself? No; Christ could not foresee that, because no Christian man will ever say that faith came of itself without the gift and without the working of the Holy Spirit. I have met with a great many believers, and talked with them about this matter; but I never knew one who could put his hand on his heart, and say, "I believed in Jesus without the assistance of the Holy Spirit."
I am bound to the doctrine of the depravity of the human heart, because I find myself depraved in heart, and have daily proofs that in my flesh there dwelleth no good thing. If God enters into covenant with unfallen man, man is so insignificant a creature that it must be an act of gracious condescension on the Lord's part; but if God enters into covenant with sinful man, he is then so offensive a creature that it must be, on God's part, an act of pure, free, rich, sovereign grace. ~ C H Spurgeon, A Defense of Calvinism
The short and sweet: Jesus died on the Cross for everyone who would ever believe in Him and be saved. He did not die for all people who ever lived. Consequently, He does not bear the sins of the damned, but only of the saved. The damned bear the punishment for their own sins.
The Biblical basis:
Isaiah 53:11 the righteous One (Christ) will make many to be accounted righteous, and He shall bear their iniquities.
John 3:16 ...whosoever believes in Him shall not perish, but have everlasting life.
The common sense: This is one of the easiest ones for me to understand, to be honest. Clearly it would be pointless to say that whoever believes will be saved, in John 3:16, if those who do not believe will also be saved. And there's the rub. Does anyone truly believe that there will be unsaved people in heaven? No Christian can, this is heresy. If someone is in heaven, they are saved, but to be saved they must believe, and it is obvious that not all people (to make an understatement!) believe. So, then, did Jesus die for the sins of those in hell? He couldn't, that would be double jeopardy. It would be unjust of God to punish someone for their sins if Jesus was already punished for them! So if there are any people in hell, then they are dying for their own sins, and that logically means that Jesus did not. Jesus only died for the sins of those who would believe in Him.
The short and sweet: If God wants you to do something, you're gonna do it.
The Biblical basis:
John 6:29 this is the work of God, that you believe Him whom He has sent.
Ephesians 2:8-9 For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, 9 not of works, lest anyone should boast.
John 6:37 All that the Father gives Me will come to Me
John 6:44 No man can come to Me unless the Father draws Him
The common sense: Of all the points of Calvinism, this is the one that seems to matter the least to me, because it's something I already take for granted. Of course God gets His way, it's writ into the whole concept of omnipotence. If God wanted to make something happen and we had the ability to prevent Him, then God would be too weak to accomplish His own will. What a puny and futile view of God that is! No, clearly if God intends to do something, then He will do it. If He doesn't, then He wasn't committed to doing it. Simple. So let's apply this: if God wants to save someone, can they resist His draw, and refuse to be saved? No. Does this mean that God saves people against their will? Here's the interesting thing: God saves EVERYBODY against their will. God isn't unfair in acting against their will, though, because everybody He 'overrules' is desiring things that will hurt them. God lets the un-elect get exactly what they want! Remember the T in TULIP: nobody wants to go to heaven. Sure they do, they just want to go on their own terms and they don't want God to be there. This is everybody prior to being saved. So when God saves somebody, He does what He knows is best for them, even though they don't agree at first! The only people who would have the right to complain that God contradicted their 'free will' are those who are saved, and the irony is that these people are in the least likely position to complain, because they received an amazing gift that they didn't deserve because of it. It's a humbling thing.
Mark Driscoll explained it perfectly in this video, by way of an illustration.
Perseverance of the Saints
The short and sweet: if you are saved, you will never become un-saved. You can be confident that you will be with God in eternity. The corollary is this: those who appeared to have been saved but now are not, were never actually saved in the first place
The Biblical basis:
1 John 2:19 They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us.
John 6:37,39 37 All that the Father gives Me will come to Me, and the one who comes to Me I will by no means cast out. ..39 This is the will of the Father who sent Me, that of all He has given Me I should lose nothing, but should raise it up at the last day.
Hebrews 6:4-6 4 For it is impossible for those who were once enlightened, and have tasted the heavenly gift, and have become partakers of the Holy Spirit, 5 and have tasted the good word of God and the powers of the age to come, 6 if they fall away, to renew them again to repentance, since they crucify again for themselves the Son of God, and put Him to an open shame.
The common sense: Again, it's double jeopardy. If Jesus died for your sins, is it possible for you to "undo" that by falling away from the faith? And if you did, and came back to the faith, then you would be crucifying Christ again--He would have died twice for your sins, which would be an injustice. No, either you were saved before, and while you seemed to fall away you were still saved, or you were not saved in the first place. This is known as a false conversion, and that's also Biblical.
Matthew 7:21-23 21 “Not everyone who says to Me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who does the will of My Father in heaven. 22 Many will say to Me in that day, ‘Lord, Lord, have we not prophesied in Your name, cast out demons in Your name, and done many wonders in Your name?’ 23 And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness!’
~ Rak Chazak