Ok, I took some pictures for future reference. This is what the bottom of the seat looks like. Note the little tabs on the suction cups. These little tabs may not be pointed in the right direction, so when you put the seat back on, turn them like this.
When you take the seat off, stick you finger under the edge of the seat, and lift the edge of the suction cup to pop the seal on both sides, and lift the seat.
When you take the seat off, stick you finger under the edge of the seat, and lift the edge of the suction cup to pop the seal on both sides, and lift the seat.