How do you write a fugue?

First, study Bach's fugues, analyze them. Consult a book on counterpoint.

The basic idea of a fugue is that there's a melody that is played alone at the beginning, and then several other voices (fugues can have any number of voices from 2 upwards) come in with the same melody. Usually the second exposition of the fugue is in a different key, most often on the 5th scale degree. Then there's all sorts of development, re-statement of the theme, reiterations of the theme, and so on. It can get very complex and they're hard to write.