Sure. Find the line out on your stereo and connect it to the line in on your soundcard. Since you are trying to work with a cassette, you can go right from the outs on the tapedeck (if the units are separate). The stereo is probably RCA out and the sound card input is probably a mini-plug. If you don't have a cable that goes from one to the other you can get one at Radio Shack, Walmart, etc. Look at the connectors and buy a cable that matches.
You can use several freeware/shareware programs to record on the PC depending on what you are trying to do. For recording/editing wav files Goldwave and CoolEdit are decent. For multitracking on the PC, N-Track is nice. Definitely enough to get started with, and will cost you little to no money.
If you have some more specific questions (or can't get it to work) post 'em.