Keep the wheel at top speed. Lay your right thumb across the top (through the center axis) of the centered clay, always keeping the clay lubricated. Push down on the end of your thumb with your left hand. Because your thumb is crossing the center, opening the clay this way ensures the opening will be centered as it is created.
Open the clay down to its final depth, about half an inch of clay at the bottom of the opening. If you aren't sure how thick the bottom is, stop the wheel and use you potter's needle to measure it.
Bring the wheel speed down to about half. Use your left hand to guide and brace your thumb. Pull your thumb outwards, with your right palm controlling the outer surface of the clay. Widen the opening to the size you would like for your pot's inner floor.
Don't make the base too narrow. Keep in mind that you need to be able to move your hand up and down in the pot's interior.