I have the answer, AND the perfect program for your vinyl needs!
Audacity Is what you are looking for.
Download it
here.
Heres what to do:
1 - Download Audacity
2 - Install Audacity
3 - Connect the "Tape Out" RCA jacks on your amp to the 3.5mm "Mic In" jack on your soundcard. (The turntable is presumeably connected to the AMP) (You must use the Tape Out jacks, Headphone jacks are pre-amplified and can fry your sound card.)
4 - Open a new project on Audacity
5 - Play the record and run over to your computer and hit the "record" button on Audacity.
6 - Wait for the song to end, and press stop on audacity.
7 - Incase there is extra length or noise in the beginning or end, simply highlight the part of the song you wish to cut and press delete.
8 - On the top menu, click "convert to....[preferable filetype: MP3, WAV, AAC, etc]."
*NOTE* if you want to convert it to a mp3, you must download a file called lame_enc.dll
Download that
here
Both downloads are free and legal. If you have any questions, send me a PM.