If the steering wheel vibrates while applying brakes this is a sure indication of misalignment between front pads and discs.
The reason why car vibrates while applying brakes
(1) Misalignment between front pads and discs.
Car troubleshooting
OK, very briefly, the steering wheel is connected to the front end and the front end is sort of "tied" to the front brakes. Since the steering wheel vibrates while braking, the problem must have something to do with the front brakes. What is happening in the front pads and discs are not in even contact when braking (i.e. misaligned), this will result in vibration. The most likely cause of this misalignment is warped front discs. However, the discs may be OK but rather the front wheel bearings are worn/loose. This would indirectly cause misalignment between the pads and discs.
What to do?
Take your car to a reputable garage and ask the mechanic to first check the front wheel bearings for wear or looseness. If the bearings are OK, you'll need to have the front brake discs machined to correct their warpage. Now, after the discs are corrected, the old pads may not "mate" or align well with the newly machined discs. So, you should replace the front pads as well.
