Basically take the line out from the tape deck or turn table and have it go into your line in or mic in on the computer. Usually that's going to be 2 (L and R) RCA jacks into a mini phono jack, so you'll need that kind of cable.
Use and recording software to record it and save out as mp3 or m4a or whatever.
If your deck or turntable go through an amp you can take the line out from there.
Special consideration needs to be taken in processing the sound from the turntable if it doesn't go through a pre-amp that removes the RIAA curve. (LPs where created with the bass range pushed up in frequency to prevent the needle from jumping on low bass notes, so you have to bring down that range with an eq using the RIAA curve. If not the music sounds tinny). It helps to have Adobe Audition or something to do that.
Details on that are here:
http://www.a-reny.com/restauration/avance.html
