It's possible to do, but basically, unless you have a digital or optical out on your turntable, and the matching input on your soundcard - to do it right requires you to plug your turntable into some sort of digital stereo reciever with network capability, which is wired to a computer running a sound recording program like Soundforge. It will take some time and a basic knowledge of both the soundforge software (or whatever you end up using), and audio mixing skills to get it to sound decent.
Plugging a microphone into your computer and just recording the song as you play it is also an option, but you won't get any stereo out of it, and it will also capture all the ambient noise around you, plus most likely it will sound like crap.
If you can just get an MP3 online of whatever it is, its much cheaper and easier just to download the damn thing.