If you've noticed the brake pedal vibrates when you apply pressure, this is not an issue you can ignore. There could be a number of factors causing the sensation, so you may want to conduct a thorough inspection of your brakes to try and find the troublesome area. Unless you're slamming on your brakes, accompanying vibrations are a sign of something going wrong. However, if you're braking a bit too enthusiastically, the vibrations could be the anti-lock brake system's response, so you'll need only to take your time stopping the car top eliminate the problem.
Most commonly, worn out or warped brake rotors will cause vibrations to travel up to the pedals. The rotors are the brake discs that the brake pads grab onto in order to bring the wheels to a stop. When this happens, the friction generated by the contact between the two parts results in high heat, which will wear down the surface of the rotor after a lot of use.
In an ideal world, the natural wear would occur evenly across the rotor's surface, but this is not always the case. When there are imperfections across the rotor, the brake pads won't be able to maintain a constant grip on the rotor. The inconsistency will translate into vibrations in the brake pedal that can usually be felt in the steering wheel as well.
In order to inspect the rotors, you will need to remove the wheel, which means you're going to need to use a car jack and jack stands to elevate the vehicle. Make sure you use the owner's manual to locate the correct placement for the jack stands to ensure you can safely work underneath your vehicle. If you're uncomfortable doing this, you may want to take your car to a professional. Whenever you're going to lift one end of your car, you should ensure the parking brake is on so the car doesn't roll away once you've elevated it. For this particular project, you'll also want to have the transmission in the neutral position.
Once the wheel is off, you should inspect the rotor for signs of wear. Since the car is in neutral, you should be able to rotate the disc by hand. Look for noticeable grooves or other signs of damage. The disc may have holes on its surface, which are there to improve performance, but one that doesn't match the others could be the source of your problem. If you see any of these issues, you'll need to replace the rotor and when you replace one, it is best to do the same with the other to ensure your brakes are uniform.
While you're down there, whether or not you've discovered the rotors are damaged, you should also inspect the other brake parts. Check the thickness of the brake pads. They should be at least one-quarter of an inch thick. You will also want to check for signs of contamination on the face of the pads, as this can affect their ability to grip the rotor. Contamination on the pad such as oil or dirt may result in slippage when you brake, which will in turn lead to a vibrating brake pedal and steering wheel.
Brake problems are the primary reason you will encounter vibrations when bringing your car to a stop, but other factors may be at play as well. Whether your vehicle is out of alignment or a part in the suspension is wearing out, these issues can lead to vibration that is only noticeable at slower speeds.