Audio's usually simpler than video in my opinion, just plug the red/white phono leads into the line-in on your sound card with an appropriate converter if necessary, and almost all sound cards, even cheap ones, will have such an input.

Just make sure in Volume Control (use the little sound icon in your tooltray), the Line input isn't muted, and the computer is set to record from that input rather than from something else your sound card is capable of. You might need to go to Options > Properties in the menu to change the recording settings as well as the playback settings. Note the Line input and Microphone input are usually different on most cards, and Line is also stereo while Mic tends to be mono.