Purchase 2 black hats. Find a hat that is firm and sturdy on the outside and lined in black on the inside so its depth is hard to judge. Stovepipe hats are a popular choice.
Cut the lining out of one of the hats and cut an oval out of it that fits snugly inside the other hat. If you can't find two hats, purchase black fabric that matches the color and texture of the inside of your hat closely.
Prepare to pull your rabbit out of the hat by placing it inside the hat and covering it completely with the false bottom you have created, before your show starts. Place the hat under your table until it is time for the trick.
Reach under the table and come up holding the hat with 1 hand firmly grasped under the bottom. Show the audience that it is empty by tilting it carefully with both hands under the bottom so you don't dump the rabbit on the floor.
Place a handkerchief over the top of the hat and say a magic word over it.
Remove the handkerchief and reach down inside the hat. Brush aside the false bottom and slide it underneath the rabbit as you grasp it underneath its belly. Pull the rabbit out of the hat and present it to your audience with a flourish.
Make the rabbit disappear again, if you desire, by replacing the false bottom on top of the rabbit when you put it back into the hat.