The best way is through a process of elimination. I would start by checking whether there is a drain in the system when the car isn't running and the key / all accessories are off. Pull the positive lead off the battery and connect a test light or an ammeter between the battery and the lead. If you have current, there is a short in the system.
This is about the worst kind of problem to find, since all the wires are wrapped in the harness. If you do have a short, the next step is to determine what circuit the short is in.
Go to the fuse block and disconnect one fuse. Then go back to the battery and check whether there is still a drain. Re-install the fuse.
Then repeat this with each fuse until the drain disappears. That fuse controls the circuit that has a short.
Yeah! You've found the circuit. Now you have to find where in the circuit there is a short. If it were me, I would start with any switches or electrical connections in the circuit.
If it isn't a short, the problem is with your charging system. Check the voltage over the battery terminals without the car running. Then start the car and check the voltage again. If the voltage doesn't go up, take the alternator to the auto parts store and have them test it. They will do this for free.
Okay I've typed a bunch of trouble shooting info, but let me go back to the beginning. Did you have your original alternator tested? How old are the battery cables and the ground strap in the car? The first thing to check on an old car is always the ground connections. Your battery and alternator can be perfect and a $5 ground cable will strand you. If they're old and ugly, I'd say replace them just to prevent being stranded somewhere at the worst possible time.
Good luck with the problem!

Please post what happens.