It's important to understand why a problem is worth solving. What data/evidence would you use to demonstrate to others that this is a problem? Who is affected by it? Most importantly, if you solve it, what is its impact?
You should be in a position that you have confidence that you'll solve a problem before committing to solve it. Have others solved this or a similar problem before? Are there known risks that you should investigate further? Should you develop a prototype?
Know your constraints. Is anything time critical; is there a deadline? Will your solution exceed a budget? Do I or my team possess the right skills to solve this?
Expect the unexpected. There will always be "unknown unknowns", future events and circumstances that you cannot predict. Consider allowing some extra time and understand how you will manage and communicate bigger blockers/delays to others.
Consider the "people factor". If you're not solving something alone, make sure you communicate effectively and early. Establish good relationships and processes.
Give some thought to what happens beyond the solution. You may have solved the problem for now, but does your solution require maintenance or additional contribution to continue to live on?
There are some of the tricks like:
1) Prioritize which things/problems to solve.
2) Apply Pareto theory.
3) Use Fish bone / Ishikawa diagram in identifying the causes of problems.
4) See if you can apply basic six sigma methods. like waste reduction...
Another issue which we encounter is information. For a particular problem at hand, do we have requisite info, complete background and data? If not, then at times we are not in a position to resolve the problem completely. So prepare your self to get as much info before you get resolving. The lack of information leads to incorrect resolution and you may not get desired results.
Yet another issue which one has to tackle is previous experience or knowledge. We as human jump to conclusions for a particular problem if we have little experience of the matter at hand. At times we may succeed and feel good but then that is a trap. We have to give good thought and have different options before concluding on one. That way the outcome would be more solid.
Hope this helps.
Your general question is very important as life presents problems in many different forms and solutions can bring great satisfaction.
I wish you the best,