There was a time when one of my dogs started gagging and I did not know what to do. I called the Vet and he said to first check his palate to see if anything was stuck there. Well, to my surprise, a big twig was stuck in his teeth, going across his palate. I was told to put my finger under it and pull. Wow, out it came and no one had to run to an ER.
I just read an article in PetPlace.com about what to do when your dog is choking. This was a very helpful piece and I had never read anything about this. In fact, I was lucky that the twig was my biggest problem as far as choking/gagging was concerned.
Here are some tips which I took from PetPlace.com which may not be complete, but it is a start when faced with this problem. Nothing substitutes calling your Vet, although having some information can't hurt:
STEPS TO PERFORM THE HEIMLICH MANEUVER FOR DOGS:
1. Clear Blockages: After determining that your dog is choking, remove any item that may be constricting the neck such as a collar or leash. Visually examine inside the mouth and remove any foreign object you see. Do not blindly place your hand down your pet's throat and pull any object you feel. Dogs have small bones that support the base of their tongues. Owners probing the throat for a foreign object have mistaken these for chicken bones. Do not attempt to remove an object unless you can see and identify it. If your pet is small and you cannot easily remove the object, lift and suspend him with the head pointed down. For larger animals, lift the rear legs so the head is tilted down. This can help dislodge an item stuck in the throat. Another method is to administer a sharp blow between the shoulder blades using the palm of your hand. This can sometimes dislodge an object. If this does not work, a modified Heimlich maneuver can be attempted.
2. Position Animal: Grasp the animal around the waist so that the rear is nearest to you, similar to a bear hug with the dog facing away from you.
3. Place a fist just underneath the ribs.
4. Compress the abdomen several times (usually 3-5 times) with quick pushes inward and slightly upward.
5. Check the mouth to see if the foreign object has been removed.
CALL YOUR VET!