Instructions
Get a quality comb. Perhaps, brushing isn't even the best terminology when one considers that most brushes are not as good at getting out mats or mats-in-development. Some brushes, such as boar's hair, are also quite stiff and can make your already touchy cat even more so. The comb should have rigid fingers, as opposed to less-durable plastic, to better rake over the hair.
Protect yourself. If your cat is particularly touchy, make sure to wear gloves to cover your hands and forearms. And don't forget long sleeves if only a portion of your arm is govered by the gloves. That way you won't be a scratched-up mess by the end of your combing/brushing session.
Don't go too easy. Make deliberate movements, so it's actually worth the time and the irritation for your cat, and so the combing is actually effective. By being deliberate you are also more careful and less likely to harm your cat by, for example, raking over a portion of the face very close to the ears (where many mats develop, in behind the ears and under the chin).
Focus. This is closely tied to #3. Turn off the TV. Turn off the speakerphone. Turn down the radio. Focus on what you are doing so you don't have a mad cat on your hands or inadvertently hurt your cat because your not paying the attention that you should.
Hold on to your cat firmly by his or her scruff. It may look like a medieval move, but it's not harmful in any way to your cat. This method is used by vets to keep animals from flailing about and to subdue them, for example, in-transport or before procedures or examinations. By keeping your pet under control, you can better do the task at hand and they won't endanger themselves or you by flailing about wildly.
How to Brush a Temperamental Cat
Most cats are very touchy. Many have sensitive areas, especially the back, which can make brushing difficult. To maintain optimum hair health, you must brush your cat on a regular basis and preferably daily if your kitty is the long-haired kind, a Persian or Himalayan among the foremost breeds. You need to get over the fear that you are hurting your temperamental cat and just do it, otherwise your pet can develop mats and even skin irritation, creating painful problems that far outweigh any annoyance or irritation that brushing may cause your pet.