What is the Calvinist view of God's sovereignty?

I agree with Jonathan, but here's a more comprehensive answer: Total depravity teaches that we are so corrupted in nature that we are unable to come to God in faith (since that would count as a good work, which we're unable to do):

Romans 8:7, 8 (NIV)
7 The mind governed by the flesh is hostile to God; it does not submit to God’s law, nor can it do so. 8 Those who are in the realm of the flesh cannot please God.

Titus 1: 15, 16 (NIV)
15 To the pure, all things are pure, but to those who are corrupted and do not believe, nothing is pure. In fact, both their minds and consciences are corrupted. 16 They claim to know God, but by their actions they deny him. They are detestable, disobedient and unfit for doing anything good.

John 6:44 (NIV)
44 No one can come to me unless the Father who sent me draws them, and I will raise them up at the last day.

Unconditional Election teaches us that God chooses us before we do anything to merit being chosen (i.e. nobody ever deserves it, but God chooses some people anyway):

Ephesians 1: 4-6 (NIV)
4 For he chose us in him before the creation of the world to be holy and blameless in his sight. In love 5 he[b] predestined us for adoption to sonship[c] through Jesus Christ, in accordance with his pleasure and will— 6 to the praise of his glorious grace, which he has freely given us in the One he loves.

Ephesians 1:11 (NIV)
11 In him we were also chosen,[e] having been predestined according to the plan of him who works out everything in conformity with the purpose of his will

Romans 9: 11-13 (NIV)
11 Yet, before the twins were born or had done anything good or bad—in order that God’s purpose in election might stand: 12 not by works but by him who calls—she was told, “The older will serve the younger.”[d] 13 Just as it is written: “Jacob I loved, but Esau I hated.”

Limited Atonment teaches that Christ didn't effectively die for everyone but only for Christians (i.e. those who would accept) - as opposed to the Arminian view that Christ's death had potential effectiveness for everyone although few benefit from it because not everyone believes in Jesus.

Matthew 1:21 (NIV)
21 She will give birth to a son, and you are to give him the name Jesus,[f] because he will save his people from their sins.” (note that He can't be saving everyone from their sins - just His people)

Romans 8:30 (NIV)
30 And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified. (note that he would not have justified those he know wouldn't accept Him)

John 17:9 (NIV)
9 I pray for them. I am not praying for the world, but for those you have given me, for they are yours.

Irristable Grace teaches us that when God chooses, He enlightens the unregenerate man and that person, understanding the Gospel, always accepts it:

John 6:37 (NIV)
37 All those the Father gives me will come to me, and whoever comes to me I will never drive away.

Acts 13:48 (NIV)
48 When the Gentiles heard this, they were glad and honored the word of the Lord; and all who were appointed for eternal life believed.

Acts 16:14 (NIV)
14 One of those listening was a woman from the city of Thyatira named Lydia, a dealer in purple cloth. She was a worshiper of God. The Lord opened her heart to respond to Paul’s message.

Perseverance of the Saints is sometimes incorrectly understood as Once Saved Always Saved. The sentiment is correct but the tone is not. Calvinists believe that true Christians will always persevere - they cannot fall away from faith if they're true Christians.

John 6:38 (NIV)
And this is the will of him who sent me, that I shall lose none of all those he has given me, but raise them up at the last day.

Ephesians 1:13, 14 (NIV)
13b When you believed, you were marked in him with a seal, the promised Holy Spirit, 14 who is a deposit guaranteeing our inheritance until the redemption of those who are God’s possession—to the praise of his glory.

Philippians 1:4-6 (NIV)
4 In all my prayers for all of you, I always pray with joy 5 because of your partnership in the gospel from the first day until now, 6 being confident of this, that he who began a good work in you will carry it on to completion until the day of Christ Jesus.

John 10: 28, 29 (NIV)
28 I give them eternal life, and they shall never perish; no one will snatch them out of my hand. 29 My Father, who has given them to me, is greater than all[c]; no one can snatch them out of my Father’s hand.

I think there are good arguments for the both sides of the debate (based in Scripture) but I personally favour Calvinism. You'll note how beautifully Calvinism fits together (indeed, that integration is required) - if we're too corrupt to accept God, then God must choose us, which means He only has to die for the ones that He knows He'll save knowing that he can save them with irrisistable grace at the right time, and knowing that the ones he chooses will always stay Christian.