There are common problems that cause your steering wheel to shake when you apply the brakes. In order from least expensive to most, they are: dry guide pins, worn brake pads, and worn rotors.
It’s generally recommended if you replace the rotors, you replace the brakes, and grease the guide pins. Or if you’re just replacing the brakes, you also grease the guide pins. Now, if your brakes are still good, you could just grease the guide pins. Most of this can be done with a basic set of tools. Replacing rotors, however, is a little more involved. In either case, this if what it takes to get the job done.
Step 1: Collapse the Caliper
Start by engaging the emergency brake, jacking up the vehicle, and placing it safely on jack stands. Open the hood and remove the lid to the master cylinder reservoir. If you don’t do this you may rupture the reservoir when you collapse the calipers. Remove the tire. Place a pry bar in between the rotor and brake pad. With firm constant pressure the caliper pistons will press back into the caliper. If you are not replacing the break pads be careful not to damage them. You could also just use a C-clamp once its off.
Note: Only do one wheel at a time. You could completely expel a piston out of the caliper. Then you’d have to bleed the breaks after putting it back.