Not sure what kind of problem you are talking about but there are a few things you can try:
Look at it from different angles to understand the problem better. Understand its properties better.
Look for its underlying causes. That is, may be you need to solve different problems!
Nibble at it. That is, solve sub problems so that you are left with a smaller (but possibly harder) problem.
Work on them subconsciously. That is, when you learn something new, let it sink in by walking away and doing something else.
Conversely, focus on the problem 100% when you are working it. If necessary, block out all distractions, including mental ones.
Look at it from a potential solution point of view. That is, if there is a solution, think of what properties it must have.
Never give up! Assuming the problem is worth solving.
Conversely, try to prove it is unsolvable so that you give up on it ASAP!
Keep notes and review them often. You may find clues in something you have already noted.
Try to explain the problem, what you have learned and your attempts to an interested person who can act as your sounding board. The process of explaining will force you to organize your thoughts and the other person can ask questions that will force you to think about cases you may not have considered. Without a sounding board and without writing down your observations you may end up going in circles.
Look at it from different angles to understand the problem better. Understand its properties better.
Look for its underlying causes. That is, may be you need to solve different problems!
Nibble at it. That is, solve sub problems so that you are left with a smaller (but possibly harder) problem.
Work on them subconsciously. That is, when you learn something new, let it sink in by walking away and doing something else.
Conversely, focus on the problem 100% when you are working it. If necessary, block out all distractions, including mental ones.
Look at it from a potential solution point of view. That is, if there is a solution, think of what properties it must have.
Never give up! Assuming the problem is worth solving.
Conversely, try to prove it is unsolvable so that you give up on it ASAP!
Keep notes and review them often. You may find clues in something you have already noted.
Try to explain the problem, what you have learned and your attempts to an interested person who can act as your sounding board. The process of explaining will force you to organize your thoughts and the other person can ask questions that will force you to think about cases you may not have considered. Without a sounding board and without writing down your observations you may end up going in circles.