The multimeter must be able to read current (not all do) and be rated high enough for your computer. You'll want to use thje amps setting on the multimeter. Amps are equal to watts/volts, so if you've got a 100 watt power supply and the battery is at 12 volts, your multmeter must be able to handle up to 100/12=~8.3 amps. Chances are you aren't going to hit the max current draw, but if your multimeter is way off, then don't try it or you'll fry your meter. (it'll just blow a fuse if it's feeling generous)
To measure current draw, put the multimeter probes in the correct holes on the multimeter for measuring amps, then put the multimeter in series with your curcuit. Something like this:
+car battery --- multimeter --- +power supply
-car battery ------------------ -power supply
Batteries are rated in amp-hours for a specific current draw. A 20 Ah battery may deliver 1 amp for 20 hours. You'll actually get a bit more or less, depending on the battery, and the total available amp-hours can change, depending on the current draw. A 20 Ah battery that runs for 20 hours at 1 amp, may run for 45 hours at .5 amps or 6 hours at 2 amps.
I don't know how much charge a battery needs to have to start the car.
I'm a tinkerer and don't have any electronics background, so my apologies if I am mistaken on any technical points, but the general concepts should be correct.