Hey, Korn!!
Tell me more.

I don't know about amps.
An amp is a receiver without the source selector switch, AM/FM tuner or any other bells and whistles. Typically an amp has a single pair of inputs and a single pair of outputs with a power switch and volume knob on the front panel. They're very simple devices and usually offer superior sound quality because there is nothing in the signal path from the source to the amp as there would be in a receiver. Cheap amps are cheap amps though, a good receiver will sound better than a bargain basement amp, that said the Class D amps are fairly inexpensive and get a lot of praise for their sound quality in spite of the low cost. They aren't monster amps though, distortion at the rated power is 10X higher than a comparable class A/B amp, it's best to keep the volume knob down low.
Specifically, how would I get the sub signal to them? Subs have their own amps.
You use the analog output on your sound card and plug each channel into it's own channel on an amp. Most amps have 2 channels of amplification (for stereo sound) you'd use a 3.5mm to RCA splitter cable and attach each channel coming out of the sound card to an amp input typically you'd put the front left and front right on one amp, the surround left and surround right on another amp, etc, keep the pairs of speakers on one amp so that volume corrections are easier to make. The sub output from your sound card would connect directly to the sub amp. Modern surround receivers have some neat room correction functions, you wouldn't have any of these functions with discrete amplifiers, but you should be able to accomplish nearly the same thing with software EQ.
And how much are they? Maybe a specific one you suggest?
You can get some really inexpensive amps on ebay or elsewhere, you really get what you pay for though, if you can afford something that isn't a bargain basement amp you'll be happier with the end result. I'd recommend any of these:
http://www.parts-express.com/pe/showdetl.cfm?Partnumber=300-380
http://www.parts-express.com/pe/showdetl.cfm?Partnumber=300-383
http://www.parts-express.com/pe/showdetl.cfm?Partnumber=300-812
not terribly impressive specs but a great price:
http://www.parts-express.com/pe/showdetl.cfm?Partnumber=310-300&FTR=
There are other amps out there, if you've got any DIY skills you can build your own either from a kit or from scratch, search gainclone for more info.
And how do I separate the signals so the I have separate directions?
Your sound card separates the signals, all you have to do is hook up the left front speaker to the left output on the amp that is connected to the left front output from the computer and so on.
I don't do LOUD, so the speakers need only a small amount of power. But I want a decent amount if it doesn't cost much more, because quality goes up with more available power, I'm told anyway.
In absolute costs, if you think you need more than 50 watts per channel the onkyo receiver you're looking at is probably the way to go. A good 2 channel amp that puts out that much power can easily cost as much or more than a 7.1 channel receiver. If you just want to hear sounds from 7 channels I think you could get away with a stack of inexpensive amps, 15w should be able to drive your speakers loud enough to be heard, you may not get chest thumping explosions, but you'll hear the sound. There's not much sense in paying for all the processing features in a HT receiver that you'll never use if you're not passing a digital signal through the receiver. On the other hand an analog amp is just an analog amp, if you think you'll ever need a digital input on a receiver it's probably better to buy a receiver that has digital inputs now instead of investing a lot in analog that will be obsolete in the future. I'm guessing by 2013 analog outputs on any consumer grade AV equipment will have vanished.