Re-amping guitar is a very popular method that modern recording engineers use to achieve sonic perfection. Quite simply, re-amping involves recording the guitar track over and over using different amps, heads, and effects. Re-amping can take place digitally, or using old-fashioned hardware methods. To re-amp, you'll need to do one thing first: recording a dry, direct version of your guitar track, which usually involves recording with a DI box between your guitar and the amp. This dry track is generally unusable, but for re-amping, it's a necessity.
From there, the track is either re-amped digitally, or via analog. Digitally, you'll use a software package -- such as Sansamp's simulators or the Logic built-in plugins -- and process that dry guitar track until you're happy. However, to truly "re-amp" the signal, you'll do it in the analog domain using a real amp.
First, you feed the dry guitar through a direct output -- doable on just about every recording interface. Then, you take that feed and route it through your desired amp combo, recording it simultaneously in multi-track. This allows you to keep trying to get your desired sound, without the guitarist needing to be present.
Re-amping is very easy, and requires very little gear. You'll need a DI box, and an interface capable of simultaneous input and output. There's some specialized products out there to make re-amping even simpler, but it's generally not necessary if you're on a budget.