Clans were added to mech battle arena to give players a way to play together on the same team, and to give players a private area to share tips and tricks. Joining a clan is achieved easily by going to the "community" page and searching the available clans. You will be unable to join a clan that has 25 members or that has blocked the addition of new members. I recommend that you don't rush into a clan, as some clans are rivals (could get you unwanted attention). Also look for familiar players, it is best to be on the same team as other players that play around the same time (international game).
Fellow clan members can be invited to join your side in a team death match. This is done in the "community" screen by using the 2nd icon on the left side of the screen, after you have selected your mech you will be sent into the match and an invitation will be sent to your clan member. This must be redone after each match. Non clan members can be invited to join you in a match if you both join a chat room with the same name.