Most people keep them in thier own tank. They will eat anything that they can fit into thier mouth.
You can either feed it live food, or if you are lucky it will accept frozen foods. Before you buy one, ask one of the employees at the store to show you that it will eat frzen foods, that way you don't have to worry about it not eating.
There are a lot of different frogfish out there, what kind are you planning on getting?