Brake rotors can become damaged in several ways. One problem is excess rust which is common for iron brake rotors. It is normal for small amounts rust to be found on brake rotors, but as this grows it becomes more of a problem and means that the brake rotors should be replaced. To try and avoid this from occurring you can avoid leaving your vehicle outdoors where it will be more vulnerable to the weather. A temporary solution meanwhile is to try removing rust from the brake rotors by wiping them down.
Another common problem is warping and this occurs as mentioned as a result of heat. Here excessive heat that comes from friction can cause the expansion of the braking surface of the brake rotors and generally results in the brake rotors becoming malformed. You might notice that your brake rotors have become warped if you notice vibration in the steering wheel or elsewhere when braking.
To repair this you can replace the brake rotors by finding a store to buy new auto parts.
Alternatively the brake rotors can be removed from the car and then put through a machining tool which will once again level the brake rotors' surfaces. Another way in which brake rotors can become damaged is if the brake pads are damaged, or if something should get trapped between them. Driving fast over gravel for instance can cause gravel to get kicked up and caught between the brake pads and the brake rotors. This then means that when you brake it will press stones against the rotors and cause damage or extra wearing. If you have a stone caught between your brake pads and your brake rotors then you make hear a crunching or squeaking noise when you drive (even without braking) and will likely find that they are not as effective as they should be. If the brake pads have become worn, you may again notice a slight squeaking noise when braking.
Other less common problems can be cracking on the blade rotors that have cross drilling or scoring.