if you hop over to the Creative Dis-signs thread, you'll find most people get a design they like, have it customized then print it out on a jetprinter (using special transfer paper) then iron it on the shirts themselves. Look for the thread initiatied by me entitled "20 steps to make" your own t shirts using dark transfers if you're interested in giving it a whirl yourself.
Of course, this is not using screen printing...
Re having them printed elsewhere, if they contain Disney images, official businesses won't touch them with a 10-foot pole because of copyright issues.