How to I play games by mail?

Play by mail games are often referred to as PBM games, and play by email is sometimes abbreviated PBeM -- as opposed to face to face (FTF) games which are played in person. Another variation on the name is Play-by-Internet (PBI) or play-by-web (PBW). In all of these examples, player moves can be either executed by a human moderator, a computer program, or a combination of the two.