For recording from an LP, you need some type of phono preamp. Many receivers have them built in and have line outputs (usually on RCA jacks). Then you take that signal and get it into your computer via one of the methods Brian suggested. If your amplifier is truely an amplifier (line in, speaker out), then a preamp is very different. Many NAD units are integrated amps, meaning they have a preamp stage. To tell, look at the back. If there's a jack that says "phono," you are golden as far as that part is concerned.
Having done this, I figured out why I don't like it. One of the "joys" of vinyl is the popping or scratchy sound that is inherent to the playback of a record. It's generally random based on dust, etc, unless you have a damaged LP. However, when digitizing, all of that noise has to be removed, or it's present on playback in the exact same place, every time. This aspect drove me nuts, so I shelved all of the vinyl until I can get a good analog setup and just enjoy them. Most of it is available on CD anyway.