Well the cheapest solution is a toneport, it has pretty good tones with the gearbox software. This is a direct line method, where you plug your guitar straight into the box, or through your effects and then to the box. The distortions are kinda weak so you may need a distortion medal if you want very high gain stuff. The other, much more expensive option is getting an interface and use microphones. This option would be if you really like the sound of your amplifier and want to capture that sound. If your amp is weak then i suggest the toneport. However if you continue recording you will probably want to upgrade to a better interface and microphones.
http://www.zzounds.com/item--LINTONEPORTGX