I just got those speakers, and yes, the orage, black, and green plugs go into your pc. I didn't have to purchase a sound card, but I did anyway and got a Audigy 2 ZS. It's relatively cheap and working out well. Idk if you have any other options than to buy a card, but look into that one.
edit: the audigy is also around $60
AMD Opteron 165 @ 2.25Ghz | Zalman CNPS9500 | DFI Lanparty UT NF4 Ultra-D | eVGA 7900GT KO SC | Zalman VF700 | 2 x 1GB Gskill PC 4000 | 2 x WD 320 GB HDD\'s | Audigy2 ZS | Logitech X-530s | Saitek Eclipse | Tsunami Dream