1996 Buick Park Avenue Car won't start

How do I tell if it is the starter, alternator or battery?
AAA gave me a charge and it started right away but when I turn it off it won't start again. The lights work, horn works, inside lights come on but when I turn the key, I only hear a click. Don't want to take it in and let them redo starter, alternator and then find out it's the battery. How can I tell?