How do you write a friend marriage leave request email?

It depends who you're asking. Assuming you're asking a professor: Start with a greeting, obviously, and then request the date/dates off that you need, being sure to let them know why. Then tell them how you plan to make sure missing those days won't be an issue (or will have a minimal impact)—maybe you'll make the work up, maybe you'll get it done early, etc. Thank them for considering, then send away. If you're requesting off at work, an email might still be necessary in addition to taking PTO—really, it all depends on your work's culture.