1 [made Community Wiki]

My first intuition is always to talk to somebody. This can help, since the speech center is a different part of the brain, works differently, taps different parts of the brain. In that way, even speaking out loud what you want to talk about can supply you with a surge of inspiration. Don't forget that written words are just a way to store the sounds we communicate with.

That said a second opinion is always very good. On the one hand someone smarter might have a ready answer, but on the other hand explaining the material (maybe from ground up, if that's not too much) to someone who doesn't know anything about it yet is apt can give you a lot of inspiration.

Try thinking about the object at hand in terms of real-life words. Ask yourself 'what happens if it does X? What if it does Y?' trying to learn a bit more about the object at hand - just like a physicist could pick up a mechanical contraption, look at it from many angles, and try turning a gear here and there, we have to do that with mathematical objects. Most of this is done on paper, using formulas and words.

Sometimes you can't put together theorems because the notation you came up with isn't intuitive enough - try thinking of a system of notation that limited to your current point of interest will be coherent, complete, and intuitive.

However sometimes some things simply will not 'tick' unless seen or heard: in signal processing you sometimes must listen to (some form of) the signals or functions at hand to understand what's going on. Fourier analysis helps visualize, but it doesn't do justice to the information you can get. In real analysis the picture of a saddle point cannot be replaced by any amount of writing - you just have to see it. Similarly an animation cannot be replaced with a few pictures. Example: I would have never noticed this effect had the display not been animated MO: effect in additive resynthesis

Try visualizing your mathematical objects. Ask a fellow geometer to help you figure out a pretty illustration. Visualizing is important because, again, it taps into different parts of our brain, all which can work for the cause rather than sitting around doing nothing. And they work better when they're looking at something pretty, rather than ugly! If you visualized the data/theorem already, try visualizing differently. Maybe you're thinking of some specific representative of the kind of object your theorem talks about, while the theorem visualizes better on a different one? (example: intermediate value theorems don't visualize too well on straight line functions..)

Another option is it might be a "writer's block". Just forget about it for some time, and get back to it later. Stop thinking about it, have a full day without working on maths, meditate, take a nap, go to the movies, sleep over it, have a good, long, enjoyable, dinner, relax listening to some music.