Measure the diameter of the pipe emerging from the floor. Select a hole saw that's the same diameter, or one that's no bigger than 1/8 inch bigger than the diameter of the pipe. A hole saw is a round cylinder with teeth on one end used to cut holes.
Cut a piece of 1/4-inch hardwood plywood using a jig saw or table saw. The plywood should be big enough to span across any holes, spaces or gaps with at least a 2-inch perimeter on all four sides of the gaps or holes if possible. If there's less than 2-inches between the wall or side of the cabinet and the pipe, measure and cut the plywood to fit snug between the wall or side and the pipe.
Measure the distance of the pipe from the wall or sides of the cabinets. Transfer the measurements to the plywood. Insert the hole saw into a drill/driver. Cut holes through the plywood to represent the pipe. This creates an opening in your plywood piece for the pipe.
Cut the plywood in half, cutting through the center of the hole. Use a jig saw or table saw to make a clean, straight cut. You should now have two pieces of plywood, each with a semi-circle where the pipe fits.
Spray one side of both pieces of plywood with construction adhesive. Place both pieces of plywood on the floor of the vanity. The semi-circle cutouts fit on both sides of the pipe to seal it or cover any holes or gaps.
Drive four, 1-inch screws down through the plywood on four sides of the pipe.