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mindspillage comments on Before you start solving a problem - Less Wrong
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One of the most useful pieces of advice I've gotten: where the solution method is not obvious, start by writing down what you do know about the problem, even the trivial bits (and then, what follows logically from that). Sometimes just seeing it all there and not having to hold those threads of thought in your memory is very helpful to making connections. Also, it is reassuring for me to see that I do know something about the problem and have somewhere to start--that my mind is not a complete blank.
I was taught to approach proofs this way. Figure out what you can derive from what you know. If the proof if is possible, one of those threads must approach the intended conclusion.
It also helps to think of statements from which your goal would directly follow, and work backwards. If one of those back-threads meets a forward-thread, you win. Still, I don't like a mechanical approach like that unless I'm certain I'm at a loss for an intuitive understanding of the problem.
Indeed, to both.