So I picked up a Yamaha YST-SW030 from a friend of mine who never used
it in the home theater system he bought, and I was wondering if it
could somehow be used on my computer sound system. I have a small
Altec Lansing setup right now, with two small speakers and a medium
subwoofer. I'm afraid I don't know too much about how speaker/sub
systems work, and I've tried other websites that have been no help at all, so advice or directions would be greatly appreciated!

lol yes of course it can :D

Just get an 1/8" stereo to dual RCA cable and plug it in to your center/sub output on your sound card (or integrated sound). Then plug 1 of the RCA ends into the sub and see if you have nice low bass, if not then switch to the other RCA and that should fix the problem. Also look around in your audio chipsets driver software and see if you can set a specific crossover point.

Oh, and I forgot to mention you also need to tell Windows to use a 2.1 configuration so that it will output sound to the sub. You can do that in Windows sound area, or your chipsets software.