I can't speak specifically to mathematical problems, but in my experience, there are two main ways to improve problem solving skills in general: 1. Practice.

I can't speak specifically to mathematical problems, but in my experience, there are two main ways to improve problem solving skills in general: 1. Practice. 2. Work on developing a better understanding of the problems you're solving. For example, if you are designing a website and all you do is memorize an html/css layout from a tutorial, then you won't be able to solve problems that develop because you won't understand why certain properties behave the way they do. Therefore, it's important to spend a lot of time figuring out why things work they way they do because by understanding those foundations, you have the material you need to solve problems.