The basic concept is that mics or instruments need to go through a mic preamp to get to the levels required by any kind of recording gear. A mixer is the logical solution for lots of inputs. Most medium range mixers (and higher end also) have either direct outputs or inserts for each available mic input (some mixers only have direct outputs for a few channels).
The direct outputs are derived from the mic input, through the internal preamp, through the mixer's eq section, and through the channel fader for each applicable channel. The direct out will usually be a balanced (+4) signal output which represents the signal coming from that channel onto the mixer master bus, and this can be used to record the individual feeds. The only issue with this is that you need to leave the faders alone during recording or your signal will be affected by the fader movement (unless you want that, I guess).
Another option is to use the channel inserts to do the same thing. You have to be careful to only plug your cables into the first click on the insert connection, though (or build special cables which is another topic altogether). These signals are usually unbalanced (-10) but are not affected by the faders, only the mixer preamp section.
For what it sounds like you want to do, the "groups" and "busses" are not an issue you need to worry about for the recording aspect (unless you need to manage more than 24 tracks, that is). The groups and busses are used for mixing, however, and there are multiple ways to use these in that process and I won't belabor the point here.
I hope this helps out. I started down this same path a couple of years ago when we started trying to figure out how to record our worship services at our church, and I'm now finally beginning to be happy with the results of what I'm able to capture.
Darryl.....
