That's what I do with my desktop->Just buy an extra cable for your guitar (to run from the amp to the computer), and a 1/4" to 1/8" adapter for the cable (guitar cable to headphone cable size). Plug the adapter to the other end of the guitar cable from the amp, and plug the adapter into the microphone port on your compy. Then, DL Audacity (free sound editing software) and use it to record input from the mic.
Gets pretty good quality of you set your guitar/amp/computer/recording volumes right
And it only costs about $15.00
BTW Audacity will let you save the sound into mp3, ogg, wav, and a few other formats in any quality setting.