Probably the most cliched magic trick in history, the old 'rabbit out of a hat' deception is a gimmick that can be done in a variety of ways. Those dedicated to pulling it off will need plenty of hours at their disposal, particularly when using a live rabbit.
Some professional magicians pull off the trick by using a combination of a trick top hat and specially rigged table, allowing them to simply reach through the hat into a compartment within the table below. Assuming you're not a big-budget pro, you will have to use more sleight-of-hand and deception as described below.
When using a live rabbit, you will need to make sure it is either docile or well-trained, as you won't want it leaping out of its hiding place--or from the hat before it's the right time. A rabbit that can actually be coaxed to keep its eyes shut is another bonus.
Decide whether you want to keep the rabbit tucked into the hat during the presentation of the trick, or kept in a handy hiding spot--such as inside a roomy magician's suit or behind a table. If the rabbit will be inside the hat during the lead-in, you're best off having the audience at least several feet away if not more; if you plan to use sleight-of-hand to insert the rabbit at a key point, you'll be able to pass the hat around for 'inspection' before its appearance.
When keeping the rabbit inside the hat, make sure to keep the hat slanted at an angle (to keep the rabbit from falling out) and make your showing of the hat (to show it is 'empty') a quick one--the rabbit should not be visible if it matches the color of the top hat's interior, particularly if its eyes are closed.
If you're planning to insert the rabbit during the trick's presentation, it helps to have a distraction that will divert the audience's attention; this can be done by having them join in a magical chant with your lovely assistant, low-grade magical special-effects (such as a small explosion of sparks or smoke) or other means. You'll still need to be smooth and quick with your movement and you can also consider using an extra top hat (tucked behind a table or prop) with the rabbit already tucked away; that way you'll simply be switching hats rather than inserting the rabbit into a hat entailing less moving parts.
All that's left now is to utter some magic words, perhaps wave your magic wand a bit for dramatic effect, and pull the rabbit from the hat to the delight of the crowd!
If you have trouble pulling this trick off, don't feel too bad--Bullwinkle never had much luck with it either!