To understand God's providence more, let's look at 1 Samuel 23:
David is on the run from Saul, who wants to take his life. At the same time, the inhabitants of Keilah are being plundered by the Philistines. David does not know what to do, because fighting the Philistines is extremely dangerous, so he asks God. God tells him to fight. David does, and he wins. Here is an example of David willingly submitting his will to God's will. He asks what God's providence will be, and God tells him. He submits (23:1-5).
The next scene has Saul knowing about the deliverance of Keilah and amassing his army to go besiege David. This is such an interesting scene: Saul's will it to take David and destroy Keilah. David asks God what will happen. God tells him if he stays in Keilah, the people there will turn him over to Saul. David decided, on this information, to leave Keilah. Saul hears about it, and does not come to Keilah at all (23:7-14). It appears God has given David an alternate future, one that was conditional, and when David made his decision, God changed the future accordingly. Some theologians say this means the God not only knows the future, but he knows all possible futures as well. After meditating on these verses, I have reached a different conclusion: God never sees the future; God causes the future to happen. Yes, he has foreknowledge, but his knowledge is of what he, himself, is going to do. Providence now transforms from a deistic, natural set of occurrences into a focused, powerful set of ordained actions on the part of God. God is not impotently sitting on the sidelines and waiting for us to make our moves, cheering us on when we make the right moves and crying when we make the wrong ones. He didn't have two possible futures that he knew and let David decide his fate. No, he give David a deeper glimpse into providence to show him how it works. If your will wins, he tells David, this is what would happen, but my will will always win. My will will have victory. Providence is God's will being played out without causing violence to our own wills. But his will is always played out, because he wills the good of those who love him.
The third instance shows this. David has left Keilah and is running around in the wilderness to avoid Saul. Saul has surrounded David, surely he will get him. But then a messenger comes to Saul, telling him that the Philistines have made a raid on his own land. So Saul departs. Here is God's providence working itself out. He did not control Saul's actions. He did not control David's actions. Capture was certain, but God's providence ordained the Philistines to attack Saul's land at that time, and the message came to Saul at that moment. God did not control the Philistines, but he made them, and he knows their nature, and he knew how they would act, and he set up secondary causes to influence their attack on Saul at that time. God did not control the messenger, but he set up secondary causes so that the messenger would reach Saul with the news at the exact right time. This is how providence works. He caused the events to happen without infringing on the free will of the people involved.
David retreats to a cave and there writes Psalm 57, where he reveals his understanding of God's providence:
Be gracious to me, O God, be gracious to me,
For my soul takes refuge in You;
And in the shadow of Your wings I will take refuge
Until destruction passes by.
I will cry to God Most High,
To God who accomplishes all things for me.
He will send from heaven and save me;
He reproaches him who tramples upon me.
God will send forth His lovingkindness and His truth.
To God who accomplishes all things for me. Romans 8:28 reads, "And we know that God causes all things to work together for good to those who love God, to those who are called according to his purpose." We see this in the ultimate good for those who love God: namely the crucifixion of Jesus Christ. In Mark 8:31, Christ teaches his disciples the he must suffer, and he must be rejected by his own people, and he must be killed, and he must rise again. This is not God predicting the future but ordaining it. These things must happen. They will happen, and nothing we will can interfere with God's plan. In fact, God's plan is carried out with the aid of our wills, because he made our natures, and he knows how we will behave and act. When Peter attempts to exert his own will over Christ's, Jesus tells him to, "get behind me, Satan!" His will will not be infringed. Once again: God does not foresee the future. He causes the future to happen. We have free will, but God's will supersedes our wills.
Jesus did not force Judas to betray him. Jesus picked Judas to be an apostle, because he knew he would betray him. He didn't see Judas betraying him in the future. He knew Judas' heart, and knew it would be his nature and will to betray him. Think of someone stronger then you. His will is going to win in a battle, because he is more powerful. He has not taken over your will; he does not control your actions like a pawn on a chessboard. He just has his way. You are allowed to exercise your will to the extent where it doesn't interfere with his. Think of renting an apartment. You can decorate the apartment with whatever you wish, live your life in it however you wish, but you can never sell the apartment. It's not yours to sell; it is the owner's. And if he plans to sell it to a developer, who is going to tear it down, you have no say. You just have to leave when the time comes. If you decide to stay and go down with the building, the plan of destroying the building has not been altered in any way. You are merely destroyed as well. Your free will has not been infringed. This is how God's providence works.
Finally, God's providence will eventually be understood and clarified to the saints in the next life. Christ tells Peter, when he is washing his feet, "What I do you do not realize now, but you will understand hereafter (John 13:7)." Individual instances of providence will be revealed to us over the course of our lives, but when we are finally with the Lord, all of his providence will be revealed, and it will astound us.