Hey there,
First, I apologize, I should have asked for the motherboard and graphics/sound cards(if applicable) that you are using also, so this will get a bit long as I'll cover most options that might be available to you.
If you are using HDMI for your video, you can send your sound through that to an AVR (video is then relayed to the monitor). A somewhat inexpensive one would be like a Denon E200, especially since this model is discontinued and places may start clearancing them soon. Another way to go would be to get a used AVR or even a refurb.
If you aren't using HDMI, but have an optical port on your MB, you can use an AVR.
If you have neither, but 5.1 out in the form of 3.5mm jacks, you can use an 5 channel amp with them, or an AVR which supports 5.1 pre-in.
Otherwise, a sound card is going to be needed.
I guess it depends on what you want to do, and what you're budget is like. What are you planning to use them for? If it's just for say music or youtube then a good 2.1 or even 2.0 setup is all that's needed. If you plan on movies with surround or gaming then you're looking more for a 5.1 setup.
Your average logitech/creative/corsair/etc PC surround system is convenient and a cheaper way to go. But I try to steer people away from that if they are looking for a more quality type of sound. Budget will determine a lot as will what speakers you already have, if they aren't very good it might be better to go with something else.
If you could list your hardware that you have (brand/model#) for MB, graphics and sound cards if you have them and what speakers you do have, what you want to do with them, and budget you're looking at, I can give you some solid options to look at. If you happen to live in a city that's listed on craigslist, I can browse the listings alittle and see if there's a good deal for used.