This type of battery drain is usually called a parasitic draw: something that stays on, drawing current from your battery even when the car is off. It can be something that kills your battery fast (having a high power amplifier staying on) or something small, that takes a lot of time to drain the battery enough to cause problems (ash tray light or glove box light) Here's how I check for parasitic draw:
Make sure you have a multimeter capable of measuring amperage. I think some cheap ones might not be able to do this. Disconnect your negative battery cable, and with your multimeter, place one lead on the disconnected cable and one on the terminal. This effectively puts your multimeter in the middle of the circuit - whatever current runs through your battery will run through the multimeter as well. With the car off and all loads off, check how much amperage is showing up on your multimeter. It should be under .050 amps, also commonly called 50 milliamps.
If you are having too much amperage, over .050 amps, start unplugging fuses one by one. What this does is cut the power to the circuits you unplug...I would start with the aftermarket alarm for sure. If your alarm is in fact drawing the current that is killing your battery, you will see the amperage go down whenever you remove the fuse. If the amperage is still too high or if the alarm fuse doesn't change anything, put that fuse back in. Then pull the fuse for the aftermarket stereo amplifier if you have one. If you have an aftermarket stereo, cut the power to that (should be a fuse or a remote wire that runs to the fuse box).
Basically start with your aftermarket stuff, then keep removing fuses until you pull the one you need out and the amperage goes down to an acceptable level. All this does is locate the problem. You will then have to look at the circuit and find the actual problem. Could be a short, could be faulty equipment, could be improper wiring. This is where expertise really comes into play...electrical troubleshooting is easy when you understand it but it can be intimidating at first. If you need help you can always come back here, or even get some help from a friend or a mechanic if you want to spend money.
I would definitely look at your alarm first, and other aftermarket equipment that is installed on your car. I bet the problem is one of those.
Of course before this test can be performed, your battery should be fully charged or close to it. If you can't get a good battery in there or if you can't charge this one, go ahead and try this test anyways to see what you come up with.
Sorry for the novel lol. Hey I just did a Google search and found something that goes over this same type of test in greater detail and some pics I think...take a look if you need mroe info!
http://www.bbbind.com/Bulletins_Attachm ... 20draw.pdf