This strategy, while perhaps most applicable to physics problems that you can visualize, still has aspects that apply to many problems. I hope it will prove useful to you.
1. Write out the problem statement in full, converting all physical units to a consistent set in the process. (That way, you can leave off the units during calculations, and simply tag them back on at the end.) Draw one small horizontal line to separate the problem statement from your solution.
2. Draw a large, clear picture of the situation described in the problem statement, applying labels to relevant quantities.
3. Identify the target variable. I.e., identify what it is for which you wish to solve.
4. Write down a correct, relevant equation involving the target variable.
5. Write down enough other correct, relevant equations so that you have enough equations to solve for the target variable.
6. Solve for the target variable, making sure not to plug in numbers for quantities until the end of the problem. After all, suppose the problem has several parts, each one "tweaking" the initial parameters a bit? This way, you only have algebraically to solve once for the target variable.
7. Set the answer inside a box with appropriate units. Write down a sentence explaining or justifying your answer.
This is the Problem-Solving Strategy. Use it! It will save you untold hours of frustration, and it will help you focus on the necessary part of the mathematics.
Hopefully, I will be able to post an example of this strategy soon.