You should get yourself a set of factory repair manuals, but in the meantime Auto Zone has information on how to replace the starter on a Firebird on their website:
http://www.autozone.com/az/cds/en_us...rInfoPages.htm
Generally, turning the key and just hearing a click means there's power getting to the starter, but only the starter solenoid is engaging and the starter itself is not turning over. As others have mentioned, most often this is caused by either a low battery or by loose connections on the battery cables (check both ends of all the cables - at the battery, and at the other ends. The negative cable goes to the engine block. I'm guessing on this because I don't have a Firebird, but the positive cable probably goes to a junction block on the fenderwell, then another cable goes from there down to the starter.) Clean all connections well - use a wire brush or even a penknife to make all the connections shiny, then put a LIGHT smear of grease on them before you put them together and make sure they're tight.
There can be enough current in the battery to still turn on the radio and to make the starter solenoid click, but if it's nearly dead it won't have enough current to make the starter work. An easy test for the battery is to take it out and try it in another car; if that works, the battery is OK, and then the next thing to check is the starter itself.
Follow the procedure described on the Auto Zone website to get it out, and take it to a local auto parts store. They should have test equipment to check it out on the bench. If it's bad it probably can be rebuilt, but since you're a novice it's probably best to get a rebuilt one from the parts store.