So you have speakers, but no amp/receiver, right?
Well, you're gonna HAVE to get an amp/receiver. That the only way to do it.
You CAN'T just "hook up" the speakers into your sound card/integrated sound (even with some kind of an adapter). Even if you could, it wouldn't have enough power to run them. And HDMI is out as well, unless you get a receiver with a HDMI input. There's just no possible way that could work otherwise.
It would work, it would just be very quiet....