True choking in pets is rare. Most people believe their pet is choking (or has something stuck in its throat), when it is actually coughing. The difference between the two is that with choking the pet has difficulty inhaling air, but with coughing, it inhales normally.
If your pet is awake, the best thing to do is to have your pet evaluated by a veterinarian as soon as possible. If your pet has lost consciousness (and appeared to be choking), perform a finger sweep across the back of the pet’s throat to remove any foreign material. Do not put your finger in your pet’s mouth if you think you are at risk for being bitten.
If your pet is unconscious and does not seem to be able to pass air, you can perform a modified Heimlich maneuver by placing the animal on its side or back, and placing your hand on its belly just under the ribcage and thrusting firmly toward the spine (while supporting its back with your other hand). Check its mouth and perform a finger sweep to remove any dislodged objects. Repeat as necessary until the object is removed, then perform rescue breathing (if needed) and transport the pet to the nearest veterinarian.