Peel away part of the backing and start at the top of the drawer. Simultaneously, press the plastic card against the cabinet and push downward inch by inch starting from the center to smooth out the bubbles before you unroll more paper. (FYI: In my experience, it is impossible to get rid of all bubbles. Don't worry, though, because people will only be able to see them if they're closely inspecting your work.)
Note: The point of this photo is to show you how to hold the plastic card as you are smoothing away the bubbles.