Hi Curious,
Welcome to the board.
I can give you a little outline with a few verses, and some opinion.
1. Total depravity (man's state)
We are basically helpless, and headed for wrath, apart from Christ. This is due to Adam's sin causing sin to enter, and all of creation and men being subject (enslaved) by the fall.
Ephesians 2:1-5
1 And you hath he quickened, who were dead in trespasses and sins;
2 Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience:
3 Among whom also we all had our conversation in times past in the lusts of our flesh, fulfilling the desires of the flesh and of the mind; and were by nature the children of wrath, even as others.
4 But God, who is rich in mercy, for his great love wherewith he loved us,
5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;)
Conditions of the sinner would be things like...
1. He is dead in trespasses.
2. Is of the world.
3. He is a slave to sin, and does not seek God in his captivity.
4. Separated from God due to sin, and is an object of wrath.
5. unrighteous, and walks in darkness.
6.lacks understanding and wisdom in God's ways.
2. Unconditional Election (the work of the Father)
This is a matter of salvation coming by grace through faith in Christ Jesus our Lord who paid the price for our sin with His own precious perfect blood. This began in eternity past as part of the economy of God. God works through the events, prophecy, prayers, and wills of men to accomplish His will. I would say that no one can be elect and not be called. The elect is he who chooses God, but it is because God called Him. He loves God, but it is because God loved Him. He obeys God, but it is because God has written His law on His heart.
John 12:39-40
39 Therefore they could not believe, because that Esaias said again,
40 He hath blinded their eyes, and hardened their heart; that they should not see with their eyes, nor understand with their heart, and be converted, and I should heal them.
1 Peter 2:7-9
7 Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner,
8 And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed.
9 But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light:
3. Limited Atonement, or a better phrase, Particular Redemption (the work of Jesus Christ)
Christ's blood is of infinite value and is also infinitely sufficent to save all that are lost, and even more, but it is particular to those who will believe...those called, and those who have choosen. All others, unbelievers, will not enter into His rest. Judgement is delayed because of God's love and longsuffering, so that all who are His may come to Him.
2 Peter 3:9
9 The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
The atonement accomplished redemption (bought back), propitiation (wrath turned), reconciliation (oneness, or peace). The atonement is the price...through sacrifice. God loved us so much that in Isaiah 53 it says that "It pleased God to bruise Him." John 13:1 1 Now before the feast of the passover, when Jesus knew that his hour was come that he should depart out of this world unto the Father, having loved his own which were in the world, he loved them unto the end.
4. Irresistible Grace or Effacious Grace (the work of the Holy Spirit)
This is the way that God calls, and this is the witness that causes one to believe on the work of Christ Jesus. This is the application of the atonement, by the Holy Spirit through the blood of Jesus Christ. This process of regeneration gives us a new nature that believes, repents, and trusts in Christ.
There are two calls, a general call to all, and a specific internal call...this one is effectual. This is through preaching, teaching, and reading of the Word of God.
2 Peter 1:10
10 Wherefore the rather, brethren, give diligence to make your calling and election sure: for if ye do these things, ye shall never fall:
5. Eternal Security, or Persevering Grace
This is simply saying that the contract, or covenant, is unbreakable. This is only for the true believer...one who has matured unto salvation. Will he sin, yes, but it is not in lawlessness. The good works are also done in Christ, and will remain because of Him. I am not trying to complicate this, but I think the parable of the sower is a good illustration of the fruit-bearing believer being one who has been elected by God to be party to this unbreakable covenant. To sum up, God's persevering grace is extended to perservering saints.
1 Peter 1:3-5
3 Blessed be the God and Father of our Lord Jesus Christ, which according to his abundant mercy hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead,
4 To an inheritance incorruptible, and undefiled, and that fadeth not away, reserved in heaven for you,
5 Who are kept by the power of God through faith unto salvation ready to be revealed in the last time.
Hebrews 10:14
14 For by one offering he hath perfected for ever them that are sanctified.
John 10:27-30
27 My sheep hear my voice, and I know them, and they follow me:
28 And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand.
29 My Father, which gave them me, is greater than all; and no man is able to pluck them out of my Father's hand.
30 I and my Father are one.
Jesus' last statement refers to His eternal covenant with the Father, I believe...their oneness in the Father's plan.
The order, I believe, is foreknowledge, predestination, effectual calling, regenetation, repentance and faith, justification, adoption, sanctification, and glorification.
I would say that this little outline is the basics of Calvinism with a few of my own opinions put in. Calvinism is misunderstood a great deal, I think. By both calvinists and non-calvinists alike. The Lord bless you.