Hang out in the forum for any length of time, and you'll hear 'I plugged my guitar into the Mic input on my laptop, and the sound is all garbled'... or something to that affect. Mismatched signal levels can lead to all kinds of sound quality problems. So it's important to understand the differences between Mic, Instrument, and Line levels. Below is a brief rundown. You might also want to browse This Article by Rane which discusses ground loops, balanced vs. unbalanced, and has a handy wiring diagram for soldering your own cables and adapters. Very helpful!
Mic Level: Microphones come in Hi-Z and Lo-Z varieties (unless otherwise noted, mics recommended and discussed on this site are Lo-Z). Mics produce a very weak signal and require a mic preamp(lifier) to boost their signals to a usable level. Plug your mic into the Mic In of your mixer/preamp where a preamp will boast the signal to a usable level.
Instrument Level: Passive instruments (no battery) produce a slightly higher signal than a mic. Active instruments (with a battery) produce slightly more. Both are less than, but compatible with Line Level. Plug guitars, basses, and keyboards into the Line In of a channel on your mixer or, better yet, a DI (direct injection) box. DI's provide ground isolation and are generally accepted to be common practice for direct instrument recording.
Line Level: Mixers, equalizers, and rack-mount effect units run at line level. Connect the Line Out of your mixer to the Line In of your sound card. Using your sound card's Line In bypasses the card's (usually quite noisy) mic preamp.
Speaker Level: High wattage output from an amplifier. Use ONLY to drive speakers.
Basic Signal Chain:
Plug a mic or instrument into your mixer or mic preamp
Run a cable from the mixer's Line Out to the Line In of the sound card (don't use the sound card's Mic In)
Run a cable from the sound card's Line Out to your monitor amp, powered monitors, or headphones
Don't have a mixer or mic preamp yet? Many find that an ordinary home hi-fi stereo cassette deck can be pressed into service with pretty good results. Simply run an audio cable from the Record Output on the deck to the soundcard's Line In, and use the mic inputs on the deck as microphone or instrument inputs. Then, insert a blank cassette, push Record, and hit the pause button. The deck's mic preamp will boost the signal and send it to your sound card. When plugging an instrument into a Mic In, be sure to turn the instrument volume down a bit.