I'm sure you could figure out the hardware part. You'll need a record player, a phono pre-amp, some RCA cables, and a sound card with audio in.

Lucky for you, there is software designed specifically for recording LPs. Here's the one I'd start with:
LP Recorder

There's also software that you can use to clean up the recordigs and reduce pops, crackles, and other noise. Here's one:
Ray Gun