Vinyl2MP3

There are a ton of downloads at Lockergnome that will help in the project.
Get a turntable with line level outputs. If you have a magnetic cartridge, then you'll need a phono pre-amp to turn that low audio level into a true line level. These are available on older-style consumer amps, receivers pre-amps and deejay mixers.
Get a cable that connects your turntable (usually two RCA connectors) to your computer's sound card (usually an 1/8th inch stereo mini plug) --- or use adaptors that match the cables/connectors you have.
Get recording software (use Cool edit 2000 or one of the downloads from the link above).
Power everything up, start recording and start the record.
Have fun!