I am a Calvinist (if I have to label myself) and I think to some extent the interplay between divine sovereignty and human responsibility is a mystery. But in some cases, I think Calvinists have been too strong in their explanations. Let me do the best I can. And of course, I think we need to look to Scripture to get the answers.
First of all, it is clear from Scripture that nothing falls outside of God's sovereignty. For that reason, to some extent, everything that happens is part of his plan. If someone commits a terrible sin, God could have prevented it if He had wanted to. Think of the terrorist attacks of 911. Could God have prevented those? Absolutely! He could have done it by changing the minds of the terrorists, but he could have done it by having them get caught before they had a chance to carry out their plan. Perhaps He did prevent one attack by using the passengers who overpowered the terrorists on the flight that crashed in Pennsylvania. Perhaps there are countless other attacks that He has prevented and we simply don't know about them. On one level, we can say that anything that happens is God's will in that He did not prevent it from happening. We can rest assured that no matter how bad a particular event is, God has a purpose and a plan to use evil to overcome evil and bring about good. We simply cannot see the whole picture. On another level (and using a slightly different definition of "God's will") we can say that it is never God's will for people to sin — He is against it and has commanded people not to do it. As a parent, I can understand this. There are things my children do that I am against. In some cases, I could physically prevent them from doing the thing that I oppose. However, even though it is "against my will" I allow them to do it because they need to learn from their mistakes. So on one level it is against my will, yet on another level, it is my will that they do what they have planned because I allowed them to do it.
Does this mean that God causes people to sin? Scripture is clear: "When tempted, no one should say, 'God is tempting me.' For God cannot be tempted by evil, nor does he tempt anyone: but each person is tempted when they are dragged away by their own evil desire and enticed." (James 1:13-14). God does not entice anyone to do evil. It is our own nature to be enticed by it. However, that does not mean that God can't direct our own evil desires in such a way that his plan is furthered.
What about free will? I believe that people are free to do what they want to do. The problem is, our wills have been corrupted by sin — we don't want to please God. "As it is written: "None is righteous, no, not one; no one understands; no one seeks for God. All have turned aside; together they have become worthless; no one does good, not even one" (Romans 3:10-12). The only way any of us will ever come to faith in Christ is that God moves in our hearts before we ever started looking for Him, convicting us of sin and of our need. When we finally "choose" Him, it is only because He has been pursuing us, and has turned our hearts toward Him.
Somehow, God is sovereign over everything that happens. Yet His sovereignty has allowed enough human freedom so that we are responsible for the choices we make, and the choices we make have real consequences. There are several passages in Scripture where we see God's sovereignty and human choice working hand in hand. The authors of Scripture can refer to both in the same context without seeing a contradiction.
Peter, preaching on the Day of Pentecost: "Men of Israel, hear these words: Jesus of Nazareth, a man attested to you by God with mighty works and wonders and signs that God did through him in your midst, as you yourselves know — this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men" (Acts 2:22-23). So Peter says that Jesus' death was according to God's plan, yet the people who crucified him are guilty.
Paul endured all kinds of hardships in his gospel ministry. Why would he do this? "Therefore I endure everything for the sake of the elect, that they also may obtain the salvation that is in Christ Jesus with eternal glory" (2 Timothy 2:10). Paul does it so the elect (those whom God has chosen to save) will actually be saved. You might expect him to say "God is planning to save certain people, so why should I go through all this hardship if God is going to save them anyway? The reality is that God has chosen to save people through the proclamation of the gospel, so Paul will go through hardship, knowing God will use it to save people.
Finally, I like this last example because it is not as theoretical or theological. In Acts 27, Paul is on a ship for Rome. I quote the text below and will make some comments along the way. Picking up in verse 13:
When a gentle south wind began to blow, they saw their opportunity; so they weighed anchor and sailed along the shore of Crete. Before very long, a wind of hurricane force, called the Northeaster, swept down from the island. The ship was caught by the storm and could not head into the wind; so we gave way to it and were driven along. As we passed to the lee of a small island called Cauda, we were hardly able to make the lifeboat secure, so the men hoisted it aboard. Then they passed ropes under the ship itself to hold it together. Because they were afraid they would run aground on the sandbars of Syrtis, they lowered the sea anchor and let the ship be driven along. We took such a violent battering from the storm that the next day they began to throw the cargo overboard. On the third day, they threw the ship's tackle overboard with their own hands. When neither sun nor stars appeared for many days and the storm continued raging, we finally gave up all hope of being saved. After they had gone a long time without food, Paul stood up before them and said: "Men, you should have taken my advice not to sail from Crete; then you would have spared yourselves this damage and loss. But now I urge you to keep up your courage, because not one of you will be lost; only the ship will be destroyed. Last night an angel of the God to whom I belong and whom I serve stood beside me and said, 'Do not be afraid, Paul. You must stand trial before Caesar; and God has graciously given you the lives of all who sail with you.' So keep up your courage, men, for I have faith in God that it will happen just as he told me. Nevertheless, we must run aground on some island."
Although they had given up hope, Paul announces that God has guaranteed that everyone on board will be spared. So you might think this means that Paul will just sit back and relax — but read on:
On the fourteenth night we were still being driven across the Adriatic Sea, when about midnight the sailors sensed they were approaching land. They took soundings and found that the water was a hundred and twenty feet deep. A short time later they took soundings again and found it was ninety feet deep. Fearing that we would be dashed against the rocks, they dropped four anchors from the stern and prayed for daylight. In an attempt to escape from the ship, the sailors let the lifeboat down into the sea, pretending they were going to lower some anchors from the bow. Then Paul said to the centurion and the soldiers, "Unless these men stay with the ship, you cannot be saved." So the soldiers cut the ropes that held the lifeboat and let it drift away.
The sailors tried to abandon ship and Paul thwarts the plan. Look at what he says: "unless these men stay with the ship, you cannot be saved." I thought God had guaranteed that everyone would live. Apparently, the way He was going to accomplish this was to have experienced sailors on board who could maneuver the ship as necessary. If they had abandoned the ship, the people could not have survived. However, in God's sovereignty, Paul noticed what was going on and told the centurion who thwarted their plan and the necessary sailors stayed with the ship.
Just before dawn Paul urged them all to eat. "For the last fourteen days," he said, "you have been in constant suspense and have gone without food — you haven't eaten anything. Now I urge you to take some food. You need it to survive. Not one of you will lose a single hair from his head." After he said this, he took some bread and gave thanks to God in front of them all. Then he broke it and began to eat. They were all encouraged and ate some food themselves. Altogether there were 276 of us on board. When they had eaten as much as they wanted, they lightened the ship by throwing the grain into the sea.
Once again, Paul encourages them to eat because they will need their strength to survive. If God had guaranteed that everyone would live, why bother with eating? Paul actually uses God's promise to encourage them so that they will feel like eating, because they need to be strong to survive what was to come. God's plan and human choices are working together.
When daylight came, they did not recognize the land, but they saw a bay with a sandy beach, where they decided to run the ship aground if they could. Cutting loose the anchors, they left them in the sea and at the same time untied the ropes that held the rudders. Then they hoisted the foresail to the wind and made for the beach.
Now we know why the sailors had to stay with the ship. The average passenger would not have known what to do in this situation. These maneuvers were necessary to get the ship close to shore.
But the ship struck a sandbar and ran aground. The bow stuck fast and would not move, and the stern was broken to pieces by the pounding of the surf. The soldiers planned to kill the prisoners to prevent any of them from swimming away and escaping. But the centurion wanted to spare Paul's life and kept them from carrying out their plan.
Once again, God had prepared things ahead of time. It would have been normal practice to kill the prisoners to prevent escape. But Paul had won favor with the centurion and he overrules the plan, saving not only Paul but all the prisoners, continuing the fulfillment of God's promise that no one on board would be lost.
He ordered those who could swim to jump overboard first and get to land. The rest were to get there on planks or on other pieces of the ship.
So, if God promised that everyone would survive, why bother swimming or hanging on to boards? Well swimming or hanging on to something that floats if you can't swim is the way that God has ordained that people normally survive getting dumped in the water. They had already eaten, so they had some strength, due to the maneuvers of the sailors, they were as close to land as possible.
To sum it up verse 44 states "In this way everyone reached land safely." — Just as God had promised, but it took a series of human decisions and actions to accomplish what God had promised.
It is a bit of a mystery. If you rely so much on God's sovereignty that you abdicate your own responsibility and get complacent, you are misunderstanding God's sovereignty. If you rely so much on human choice and responsibility that you become fearful that God's plan may be ruined, then you are also misunderstanding God's sovereignty.