You will need a soundcard, some cables and software.
The soundcard you probably already have as part of your computer system. You need to plug your stereo system (i.e., turntable/receiver) into the "line in" jack on your sound card. Generally you will connect from the "line out" or "aux out" connections on your receiver. I am assuming these connections will be RCA plugs, and therefore you will need a Y cable to connect up to your soundcard (two female RCA's by one 1/8" male stereo plug). You should be able to get the Y cable at Radio Shack.
Once you have physically connected the computer and stereo systems together, you need software. The one I am familiar with is Spin Doctor (which is a component of Adaptec's EZ CD Creator Deluxe package). There are many others out there as well.
Once you have the software, the rest should be pretty easy. The software will create .wav files on your computer, which you can play using Windows Media Player (or Win Amp, etc.), or which you can use to burn CD's (if you have a CD burner).