I would think about different aspects of the problem a lot. How they manifest themselves, which of them I could possibly tackle and which are beyond my comprehension at the moment. Eventually I get enough resolve to approach and make an attempt on those that seem reachable. This almost inevitably clears up just a bit of the nature of other aspects, so that after another period of contemplation you can in turn tackle on them.

So basically, look hard at the problem, chisel it a bit and back off for a moment. If you can't solve it right away it's a substantial task that has to be treated with respect. Naturally this process is poorly suited for meeting deadlines.