You might have an easier time remembering recognition principles instead of memorizing the precise statement of a theorem. For example, you might want to remember that Theorem X can help you if you have data Y about structure Z and want to prove something else about it. It is also useful to remember references this way, e.g., "This is the sort of result that would be proved in So-and-so's paper or works cited therein." If you find yourself using a theorem a lot, chances are that you will become more comfortable with the precise statement with time.
If you want to understand more context surrounding a theorem, it helps to talk about said theorem with other people. In addition to traditional avenues of conversation, this can include volunteering to lecture on it, blogging about it, or possibly asking questions on Math Overflow.
