[douglas]

By memorizing the initial configuration and using a lot more moves than are normally necessary. The farther along you get in solving a Rubik's Cube the more you have to worry about not disrupting what you've already done. There are a bunch of somewhat long sequences of moves that end up changing the positions and orientations of a very small number of cubes (even as low as 2 or 3) while putting everything else back to where it was before you started the sequence. Normally you would use these only near the end of the solution, but blindfolded solvers use them from the beginning so it's easier to keep their memorized model of the cube up to date.

Note: I can solve a Rubik's Cube, but not blindfolded, probably not with one hand, and definitely not in 20 seconds. I haven't timed myself, but I think I'm somewhere in the "less than 5 minutes" range.