To play a Tower Duel with a teammate you need to be part of a team. You can either create or join an existing one -for more information about how to become part of a team, please read our articles How can I create a team? and How can I join a team?
If you are already part of a team, you'll be able to see the list of members and their activity, that is, if they are online or offline, in the main tab. Along with their names, you'll be able to see the number of medals they have, their levels and a third option featuring the Tower Duel icon. If you tap on this last icon, you'll be able to play a Tower Duel with the teammate you choose, as long as they are online.