An Alliance allows you to be in a group that can chat within the game, Request a Knight to have an extra Hero to explore any Places of Legend, and use Sea Trading as a means to exchange items.
When running an Alliance, you choose your Alliance's name and a Motto.
Using Facebook groups, Zynga's blogs / forums, searching the internet for other players is the way to go, whether recruiting for your Alliance, or looking for an Alliance to join.