If you have a Mac, check out Freeverse's Sound Studio 3 at www.freeverse.com/soundstudio . Last year I used the program's v. 2 to transfer old D'Oyly Carte and Metropolitan Opera recordings to the Mac with with great results and minimal fuss, although - as NH mentions - it took a while to input then clean up the pops and crackles.
The only special equipment I needed were things I had already: turntable, stereo receiver, a stereo RCA to 1/8-inch miniplug cable (one end connected to the receiver's audio out, the miniplug end into the Mac's audio-in jack). I used headphones rather than listened through speakers, to minimize any possible sound delays.
An article detailing all the steps was in the July 2003 issue of MacAddict magazine. (Of course, the newer version of Sound Studio probably makes the whole process easier.)
Be aware that if you input as AAC (which was best for the classical music I transferred), you've talking huge file sizes.