If the battery is dieing from just SITTING, you likely have a short somewhere. If the battery dies after some driving and can sit relatively ok, your alternator/char
I just went through this with my van. Battery died with the van off and the radio on for more than 5 minutes. Literally jumped it all the time. I replaced the battery, battery didn't work. Found out it wasn't charged when I bought it (as a lot of places don't pre-charge them now) so I charged it and it worked fine. Check with the place you bought it from and ask if all batteries are pre-charged. If not, bring it to them to charge it for you if you don't have a charger handy. Double check all the fuses are good while you are at it.
Secondly, if the alarm/starter is aftermarket or was installed by anyone other than a professional alarm installer, you very well might have something draining the battery constantly. I hear more problems from people with alarms than anything else when it comes to dead batteries.
Thirdly, once the battery is charged, the voltmeter (read the instructions how to check voltage with DC volts) should read between 12 and 13 volts across the battery posts while it is running. This indicates the alternator is functioning. If you shut it off it should be just about 12 volts. If you test it again in about 30 minutes and it already falls below 12 or 11.5 volts, there is definitely something draining it. Lastly, check to see if the glovebox light is on, or some odd light in the back of the car or in the trunk or what not. Sometimes all it takes is one little light to drain a battery. Or a faulty install of an alarm system...
Just for sake of safety, make sure the connectors on the posts of the battery aren't corroded. Use just plain ball bearing grease or vaseline after cleaning them with a wire brush (or replacing them altogether).