i did a quick google and believe i found your system specs:

alienware m9700
http://www.alienware.com/customize/a...de=SKU-DEFAULT

memory says:
2GB Dual Channel DDR SO-DIMM at 400 MHz — 2 X 1024MB

but you said: My rig is a Alienware m9700, Geforce 7900gs. AMD Turion 65 mobile. 804 MHz, 1.00gb of RAM

so either your a bit off on your current memory, or you got it when they were shipping with 1G instead of 2G.
(run dxdiag from the start/run menu to check system specs.. just type it in and run)

i'm not exactly sure what the max memory capacities would be for this box, but hopefully someone else will chime in. otherwise, call alienware directly and ask them what the biggest single chip it can take would be (1.800.alienware)

you could also ask the alienware rep if they would ship you the memory... insuring you get the right stuff (hopefully)

installing laptop memory is usually easy... a couple of screws on the bottom of your laptop, pop out chips (gently) and put in new ones (standard caution against static, of course)

good luck,

Rob