The first step is to reveal details of the fog machine. If it's dmx controlled then you may be able to control it simply. If there's no dmx control then you are going to have to use a relay driven off a dmx dimmer or something like that.
The brand and model is just about the minimum info.
Maybe OP doesn't have a fog machine yet... if not make sure to get one that supports DMX, as the k32 (and many other controllers) support this.
From that point, yes, you need the manual to know how to set the channel, what the channels do. Then you can make a DMX model in xLights on your controller serial port, and put DMX (or even "On" effects, if the setup is really simple) into the sequence.