All good suggestions, some for maintenance, some for troubleshooting, however, Scott is right on. If you don't have all that available, you can start the engine, and then unhook the ground cable from the battery. If it dies, it's the altenator. If it continues to run, then it is the battery. By all means, Scotts's suggestion for NAPA is good. If you live in the south, Auto Zone sells a lifetime altenator, and they don't haggle when you take it back. I did it not more than 4 months ago.
FOR ANYONE READING THIS, DO NOT DO THE ABOVE TEST WITH A GM PRODUCT_IT RUINS THE BUILT IN REGULATOR.
This is a simple remove/replace situation.
Now, if you think something is staying on, or that there is a short, get a cheap 12v
test light. Go to the fuse box, and pull the fuses one at a time. If the light burns when you test across the two fuse receptacles, unless it should be pulling power all the time (computer, brain for sound system, clock etc) then you have found your drain.