Empty the Tank
Turn off the water at the toilet stop by turning the handle clockwise. Drain the tank by pulling on the handle. Take a sponge and bucket to soak up the remainder of water left in the tank. If needed, use some paper towels to finish the job.
Now that the tank is empty, it's time to address the bowl. Since there's still water left in the trap, take an ordinary plunger and press it once or twice as you would with a clogged toilet. This will force all the water out of the trap making the old toilet ready for removal.