A fan letter to an actor or a band? Tell them - why you wanted to write to them
how you think that they are the best/ coolest/ most adorable actor/band in the world/ solar system/ universe
which piece of their movie/ series/ album/ song/ you like best and why
what sort of movie / series you'd like to see them on / what sort of song you'd like to hear them sing
Well, you definitely don't want to sound like a crazy, stalker girl. Be appropriate and delve into just a few compliments, and tell them how they inspire you.