Well okay, first you have to charge up your battery on a charger. That should get the car running. Then you can test the alternator with a volt meter (should read over 14 volts and should raise the needle or digital readout as you rev the engine and drop it as you idle the engine).
If you have a fully charged battery but the car remains dead, nada, nothing---you'll have to check your cables for tightness or signs of corrosion.
If you charge the battery and the engine cranks and cranks and cranks, it's not your alternator giving you grief.
You may need to have the trouble codes read as well, to give you a hint as to what might be going on here.
But generally you may be on the right track---if the alternator wasn't working, your battery would drain and drain and drain, and eventually there wouldn't be enough voltage to run the car properly. It would start to stumble and fail, and eventually your battery would drain to zero.