You can still use your computer's sound card but it will be a lot better to get one made for recording.
The signal chain would be:
Microphone -> Preamp -> Mixer (optional) -> Sound card
Most outputs on preamps are 1/4". Most inputs on normal sound cards 1/8". So you need a 1/4" to 1/8" adapter. They are like $2-$3 at Radio Shack. You just hook it onto the end of the cable and then plug it into your sound card's Line In jack.