How do I play correspondence? (Android)

Log into ICC on your Android app and go to the top-left menu and select "Correspondence".  After you are in the correspondence section, click on the mail icon and choose your opponent.

A correspondence game can last for many weeks or months. You can spend several days planning your move. The time control for correspondence games is a minimum of 1 move every 10 days. You will be sent an email and message if nine days pass with no move, letting you know you have less than 24 hours to make your next move in the game(s) in question.