Battery Dead/no output from alt

Ive got 2003/3.0/24vdohc.while the engine running theres only 11.9volts at the battery[2 mon old].I think its the alternator? The ? is how do you get it out,and is there any thing else i can check like does the alt shut off went the voltage drops? I think i left the doom light on over night

The alternator should be pumping out 13-14 volts as measured at the battery while the car is running. Your alternator is probably bad and that's gonna kill every battery you put in. Autozone (I think) will test the alt. for free.