Brake chatter or shake felt in the steering wheel when the brakes are applied is usually caused by the brake discs (also called rotors) being out of true or no longer having parallel surfaces that the brake pads contact when the brakes are applied.
The problem may be more noticeable when you are braking coming down hill.
The brake discs can be machined to bring them back into a serviceable condition provided they are "thick enough" to have material machined off them. If they are do not have material that can be removed the brake rotors will have to be replaced.
Worn suspension bushings can also be a cause for shuddering in the steering when the brakes are applied.
"Chatter" a noise only may be due to contamination on the brake discs, cheaper quality brake pads or missing or dislocated brake hardware.