The first principle of problem solving is to get the facts. It's in the Bible, Proverbs 18:13, TLB. "What a shame—yes, how stupid!—to decide before knowing the facts!"
The second principle of solving problems is to be open to new ideas. It's in the Bible, Proverbs 18:15, TLB. "The intelligent man is always open to new ideas. In fact, he looks for them."
The third principle of problem solving is to hear both sides of the story. It's in the Bible, Proverbs 18:17, TLB. "Any story sounds true until someone tells the other side and sets the record straight."
How does God want us to respond to problems? Realize that problems are inevitable and grow as a result of them. It's in the Bible, James 1:2-4, NIV. "Consider it pure joy, my brothers, whenever you face trials of many kinds, because you know that the testing of your faith develops perseverance. Perseverance must finish its work so that you may be mature and complete, not lacking anything."
Problems are confirmation that we are being prepared for heaven. It's in the Bible, II Thessalonians 1:5, TLB. "This is only one example of the fair, just way God does things, for He is using your sufferings to make you ready for His Kingdom."
How can we handle problems? God can help us with them. It's in the Bible, Psalm 145:14, NIV. "The Lord upholds all those who fall and lifts up all who are bowed down."
Jesus can sometimes free us from burdens and problems. It's in the Bible, Matthew 11:28, NIV. "Come to Me, all you who are weary and burdened, and I will give you rest."
Trust that God's ultimate purpose for your life is good. It's in the Bible, Romans 8:28, NIV. "And we know that in all things God works for the good of those who love Him, who have been called according to His purpose."
Hard time solving your problems? God will help. It's in the Bible, James 1:5, TLB. "If you want to know what God wants you to do, ask Him, and He will gladly tell you, for He is always ready to give a bountiful supply of wisdom to all who ask Him; He will not resent it. But when you ask Him, be sure that you really expect Him to tell you, for a doubtful mind will be as unsettled as a wave of the sea that is driven and tossed by the wind; and every decision you then make will be uncertain, as you turn first this way, and then that. If you don't ask with faith, don't expect the Lord to give you any solid answer."
Trust in God rather than self for guidance. It's in the Bible, Proverbs 3:4-6, TLB. "If you want favor with both God and man, and a reputation for good judgment and common sense, then trust the Lord completely; don't ever trust yourself. In everything you do, put God first, and He will direct you and crown your efforts with success."