Tips on learning how to write proofs

In mathematics, proofs are all the rage. I’m currently TAing a course on theory of computation, which is the most math many students have seen in the last four years, and definitely not high school style mathematics (i.e. ‘shut up and calculate’). So I’ve been asked some tips on how to cope with proof writing and I ended up writing quite a long ‘guide’, which I like enough to publish here, for the public to ridicule.

This is a companion discussion topic for the original entry at