It always helped me to bear in mind that the instructor believed that everything I needed for the exam had been supplied in the course. So I shouldn’t have to reach out into space for answers. Also before writing a blue book essay I would pause long enough to think through my main points and make a little mental outline rather than just starting to write like mad.
Staying calm helps a lot. Think of Worf on the bridge when the Enterprise is going to blow in 18 seconds unless he performs the right sequence: this is no time to lose your head.
One thing I noticed in the course of taking very many exams is that sometimes the clue to one answer is in another question. I strongly suggest reading through the entire exam before starting to write.
After several decades away, I am back in the student’s chair and anticipating more blue books and papers, so now I’ll find out if many years of a career and many life lessons are of any use when it comes to doing academic exercises. If they are, then I should be a gold mine of tips; if not, then we’ll see how well some things stick. pdworkin might have some pertinent thoughts on this point; like me, he is an old guy back in school, but unlike me he is doing it for career reasons, whereas I am just in it for fun.