Your brakes will develop rust; there is really nothing you can do about it. Even washing your car will cause rust to build up along the brake rotors or outer brake drums. The good news is that this is cosmetic damage for the most part, and most of it comes off very easily. If there is any rust you need to personally remove, it should only be because you're concerned with the car's appearance.
Drive the car and apply the brakes frequently. This will remove a vast majority of the rust, especially on the brake rotors.
Remove the wheels to access the brakes if you need to remove any rust personally. Using the stock lug wrench and jack or aftermarket versions, loosen the lug nuts, raise the end of the car with the jack and remove the nuts to remove the wheel.
Apply brake cleaner to all the brake parts, using a dripping pan to catch all residue, and wipe as much rust off the edges of the brakes as you can. Try rubbing the rust off again after the cleaner evaporates.
Switch to a wire brush--steel or brass--and scrub the brake parts with it. Applying more brake cleaner before scrubbing can help.
Disconnect the main brake parts if the above methods don't work so you can soak them. For brake rotors, disconnect the caliper and its bracket from the rotor by removing their bolts with a ratchet or hex wrench--it can vary--and pull the rotor off. For brake drums, cut off the pressed washers on the studs with a metal cutter and slip the drum off. (Replace with new washers when you're finished.)
Soak the disconnected brake parts in a container of liquid cleaning concentrate mixed with about a gallon of water. Make sure the rotor or drum is dry before attaching it back on the car.
Some aftermarket brake rotors are specially plated to repel rust. You could paint the brakes with Rustoleum or a similar water-repellent paint. However, do this only if you can successfully paint the areas that the pads don't touch, or the paint can damage the brakes.
Using an oil-based cleaner like WD-40 is not recommended unless you are absolutely sure you can remove all of the lubricant from the brake parts.