A major cause of difficulty in solving problems is the habit of trying to "see the solution" in one's head before writing anything down.
To avoid falling into this pit, make extensive use of scratch paper when solving problems. Always use pencil, and keep a good eraser handy. A couple of colored pencils can be extremely useful. Here are some simple steps to follow:
In another location on the scratch paper, write, again in your own words, a description of the answer required.
At first, you may be uncomfortable with this approach, perhaps seeing it as artificial or slow.
However, if you use it regularly when you study, so that it becomes familiar, you will find that when you start to work on an examination or problem set, instead of sitting and staring blankly at the questions, you will automatically begin to write.
Getting something of your own down on paper is crucial in problem solving.
Once you get your thought processes flowing in their logical track, the problems then will seem easy.
This technique also can aid you in thinking on your feet. For example, when you go to the board in a class to solve a problem, start out as described, but using the board rather than a sheet of paper. Restating the problem not only will help you begin to think along a proper track, but assist the others in the class in following along.
This last point leads to another issue. When you are teaching, you must work problems in a way that helps the students to learn, not just the subject matter of the course, but also how to solve problems common in that field.