Here's the way I do it, for what it's worth ($.02 libyan)
1. I hook my turntable into my tape deck (a 4-channel cassette mixing deck I got for under $200 at the music store). The turntable has no pre-amp, and it's a ceramic (i.e. quiet) cartridge, but the tape deck can take very high impedance microphones, so the signal from the phonograph is more than enough. This requires two adapters that are rca-female to 1/4" (mono) phone male. The rca-female attaches to the rca-male of the phonograph's output; the 1/4" mono male plugs into the tape deck.
2. I then hook the tape deck up to the "line in" jack on my PC's sound card. This requires one adapter that is 2-rca-male on one end and stereo 1/8" male on the other. The rca-male plugs plug into the tape deck; the 1/8" male phone plug plugs into the sound card. I set all my sound levels and record directly to Cool Edit. If I'm doing other stuff I let it just record the whole side of the tape and come back and break it into individual songs later; if I've got the time I'll sit and listen while I record, and stop the deck and do the cleaning for each individual song (cutting away lead-in silence and pruning the tail-out silence so that it duplicates the timing of the phonograph record without lead-in time (when the cd player counts backwards) between tracks).
3. Then I burn the CD from the wav files.
4. Then I turn the wav files into MP3's and throw the WAVs away (they take up a LOT of disc space). My encoder of choice is Mthreedev's "WAV to MP3 Encoder" version 1.5.1. Freeware. Works like a charm.