Question: "How does God's sovereignty work together with free will?"
Answer: It is impossible for us to fully understand the dynamics of a holy God molding and shaping the will of man. Scripture is clear that God knows the future (Matthew 6:8; Psalm 139:1-4) and has total sovereign control over all things (Colossians 1:16-17; Daniel 4:35). The Bible also says that we must choose God or be eternally separated from Him. We are held responsible for our actions (Romans 3:19; 6:23; 9:19-21). How these facts work together is impossible for a finite mind to comprehend (Romans 11:33-36).
People can take one of two extremes in regard to this question. Some emphasize the sovereignty of God to the point that human beings are little more than robots simply doing what they have been sovereignly programmed to do. Others emphasize free will to the point of God not having complete control and/or knowledge of all things. Neither of these positions is biblical. The truth is that God does not violate our wills by choosing us and redeeming us. Rather, He changes our hearts so that our wills choose Him. "We love Him because He first loved us" (1 John 4:19), and "You did not choose me, but I chose you" (John 15:16).
What are we to do then? First, we are to trust in the Lord, knowing that He is in control (Proverbs 3:5-6). God's sovereignty is supposed to be a comfort to us, not an issue to be concerned about or debate over. Second, we are to live our lives making wise decisions in accordance with God's Word (2 Timothy 3:16-17; James 1:5). There will be no excuses before God for why we chose to disobey Him. We will have no one to blame but ourselves for our sin. Last but not least, we are to worship the Lord, praising Him that He is so wonderful, infinite, powerful, full of grace and mercy—and sovereign.