How much money do rally drivers win?

In the US, generally nothing. In other parts of the world, generally nothing. For the World Rally Championship, generally nothing.

The ecosystem of rally is not built around prize money. At the world level, there are usually five or six guys who are getting paid to drive, and everyone else is paying the manufacturers to be there. In the US, in any given year there may be one or two people for whom driving is a job. A couple dozen others may get a couple hundred dollars per rally in contingency money from vehicle manufacturers like Mazda or Subaru.

Rally is a hobby, and while many of the cars look like they have big sponsors simply because there are very nice vinyl graphics on the car, the truth is those are generally not high dollar, cash sponsorships. More common is an arrangement like "Make your rally car look like I sponsor it, and I'll sell you parts at my cost instead of the regular markup."