Disclaimer: be sure to follow any copyright restrictions on tapes you are about to record!
For many current Macs, you have a 1/8th inch audio jack available for input. For those who don't have one, using a
Griffin iMic will let you get beyond that limitation.
Either way, you can use a standard 1/8th inch to 1/8th inch cable like those found at Radio Shack (links to example cable).
If the tape player doesn't have a headphone port to connect to that type of cable, you can probably get an adapter so that it does connect. Once you have that, the software called Audio Recorder records direct to MPEG-3 or AIFF. Together with the Lame Encoder, Audacity works quite well to edit MPEG-3s.
Note: some headphone ports don't have enough power to give audio of the strength needed for the audio input of certain machines. If it doesn't Audio Recorder will show no input. Ensure that Apple menu -> System Preferences -> Sound -> Input has the line in selected before launching Audio Recorder and after connecting the cable. For those where the input isn't sufficient, sometimes using a Griffin iMic is better, and sometimes you may need some audio amplifier, as the audio in port of the Mac is a line-level audio input.