Connect your turntable to the phonograph inputs of your stereo amplifier, if you haven't done so already.
Bring your laptop close to the stereo. If you don't own a laptop, bring your stereo to your computer or your computer to your stereo---whichever one is more portable. Connect the RCA tape outputs from the stereo amp to the 3.5 mm (1/8-inch) line input of your computer using a stereo cable with two male RCA jacks and one male 3.5 mm headphone jack. On PCs, the line input is usually colored blue.
Start up the recording software on your computer, set it to the Red Book CD standard of 16-bit, 44.1-kHz WAV files and click the record button.
Select the vinyl album you wish to record, put it on the turntable, drop the needle and play it through the stereo at any volume you wish. It won't affect the recording volume since that's controlled by the recording software.
Make sure the software is recording at a high enough volume level. If not, adjust it manually or set it to automatic. If adjustments need to be made during the first song, you can keep the recording going on the computer---just make sure to start the vinyl album over from the beginning.
Edit the resulting single WAV file on your hard drive into several smaller WAV files, each containing one song. The software should also allow you to trim the beginnings and ends of each song to eliminate clicking and popping noises from the needle.
Add the WAV files to your iTunes application, set the import preferences to MP3 and convert these WAV files into MP3s. You may now burn the WAV files to CD and add the MP3s to your portable player.