How do impulse response guitar amp simulators work?
When talking about modeling, there are two things that usually get modeled: 1. the guitar amp, and 2. the speaker cabinet. Only the latter is modeled by an impulse response, which means that the cabinet is simply represented by an LTI system and implemented by convolution. This is of course an approximation but it works fairly well. You can find a lot of such measured impulse responses on the internet.

As for the guitar amps, there is no such thing as an "impulse response guitar amp simulator". As mentioned in the comments and in Marcus Müller's answer, guitar amps are much too complicated to be modeled by a simple impulse response. They are non-linear and dynamical, and the corresponding digital models are quite complex. There's a good reason why the big players in amp modeling (Kemper, Fractal Audio Systems, Line6) do not publish their modeling algorithms.

There are two basic approaches to modeling of nonlinear analog circuits: 1. black-box models, which only try to emulate a measured input-output relationship using a set of test signals, and 2. white-box models, which try to simulate the actual analog circuit in all details.
You can read a good summary of the basics in A Review of Digital Techniques for Modeling Vacuum-Tube Guitar Amplifiers.