Like Java programming, problem solving is also a skill. There are a lot of resources out there that teaches you how to use Java to design your solution. The harder part of your question is learning the process of problem solving.
The first step is usually understanding the problem itself. It sounds simple, but it’s probably the easiest step to get wrong. Here are several ways to “understand” the problem to get you started.
5 whys - Ask why 5 times, you will usually end up with the root cause? Solving that would probably resolve a lot of the symptoms.
Mindtools.com - Problem-Solving Techniques - lots of great tools and techniques here.
Once you get that sorted out, the process of designing good solutions would probably requires understanding of algorithm. Effective Java programming would need good understanding of frameworks and the gazillions of libraries out there. The right tools for the right problem.