First off, it sounds like you're new to this, so like I tell everybody, try not to get too dismayed if all of this gets frusterating and doesn't sound good. Lots of work and patience is what it's all about.
Also, I'd like to mention that you really really REALLY should get some monitor speakers. Using just your computer speakers, you'll be able to get your mix to sound good, JUST ON YOUR COMPUTER. Monitors are designed with a flat response so that it'll sound good on almost all systems. If you plan on distributing your music, moniters are a must. I can't tell you how much my mixes started to improve once I got a decent set of monitors.
When my band records stuff, we do drums first. Generally that's the easiest. Set up your guitarist (or who ever really leads the songs) with an amp, and then plug in the headphones and give those to your drummer. Make sure the drummer clicks it off (RECORD THE CLICKS!!) and then go from there. Once you have the drums, you can fit in everything else pretty easily in whatever order works best. Anyway, drums first is just what's worked best for me, so if something else works better for you, go for that.
A preamp processes a signal and gets it ready for, you guessed it, amplification. For a basic explination, I'll use a guitar and a guitar amp as an example:
Guitar --> Preamp --> Power Amp --> Speaker
That's generally how it works. Your guitar makes the noise, the preamp does all the sound changing (distortion, effects, tone, etc.) *(there's a lot more that affects tone, I'm just trying to simplify this)*, the Power amplifier boostes the signal a couple thousand times so it's powerful enough to push the speaker, and the speaker takes the electric signal and turns it into an acoustic one that you can hear.
So what's all the talk about it in recording? Well, if we're talking vocals, you're probably using your mixer as a preamp right now. It takes the vocal signal, changes the tone, and makes it louder/softer depending on how your volume is set. If you go straight into your sound card with no preamp, you can run into lots of different voltage, volume, and tonal problems.
For guitar, the preamp used is usually in your amplifier. Some people prefer to let the amplifier go the full route and then just mic the amp, while other people choose to use Direct In (DI) recording, where you go straight from your preamp to your sound card. This can be done through either a line out on your amplifier or a "DI box" specifically designed for this application.
Anyway, before I go on for too long here, the point is, preamp is what shapes the tone, sets up the voltage, and controls the record volume.
And for all you experts shaking your head, yes I do realize I oversimplified everything for this explination.
