Here is a small section from my book on Pet First Aid:

Pet First Aid Secrets: Complete Canine And Feline First Aid Manual is a 275 page manual (in e-book/digital format) on Essential Pet First Aid Skills for Dog and Cat Owners. Covers 64 First Aid situations

SIGNS

The signs of choking are much the same as a person. Your dog or
cat is struggling to breathe, with their mouth open. They may
be pawing at their mouth. 

They may be attempting to vomit.

You may hear an unusual sound as they attempt to breathe and
pull air through a foreign object lodged in their throat.

CAUSES

The causes of choking are with anything that can lodge in the
throat. This is fairly exclusive to dogs – cats are usually
more particular. An example would be a dog fetching a ball,
and having it lodge in their throat. A variety of food objects
can lodge in your pet’s airway.

SOLUTIONS

CALL YOUR VET IF NEEDED. Dogs are notorious for trying to
swallow things that are a little too big. The result can be
choking where an object lodges in the airway.

REMOVE THE OBJECT. When time is of the essence, you must
act quickly.

Open your pet’s mouth:

* Open your pet’s mouth
* Grasp the upper jaw with one hand over the muzzle.
* Press the lips over the upper teeth with your fingers
on one side and the thumb on the other so that the dog’s
lips are between its teeth. Firm pressure may be required.
The dog then can’t close its mouth without biting itself
and is less able to bite you. Pull his tongue out of the way.
* Reach deeply in to the back of your pet’s throat and try to
grasp the object. If it is a ball, and you are unable to move
it, try using some type of instrument; tweezers, pliers or even
a spoon shaped tong.

Lay your pet on its side. For small pets, place your palms
behind the last rib on both sides of your pet’s abdomen and press your palms together quickly 2 – 3 times. Repeat if necessary. For larger dogs, place both hands behind the last rib and push down and slightly forward sharply. 

WITH both arms, give sharp thrusts to the abdomen.

AFTER 5 thrusts, stop and check to see if the object is visible
in the airway. If so remove it and give 2 mouth-to-nose rescue
breaths. 

If the breaths do not go in, repeat HEIMLICH.

In some cases, your dog is too large to pick up. You can lay him
on his side, and make a fist. Put your fist into the hollow
beneath the rib cage, then push firmly inward and upward.

Repeat 5 times, and then check to see if the object has been dislodged.
If after a few attempts it is still lodged, but you can still hear wheezing and some noise when your pet is breathing, then you have time to rush to your vet.

CPR. If your pet completely stops breathing, then you will have
to know the CPR steps.

After the airway has been opened, you may need to give artificial
respiration.

CLOSE your pet’s mouth and breathe directly into his nose until
his chest expands. 

If the chest doesn’t expand then go back to STEP 2 – AIRWAY.

VENTILATE at 8 breaths per minute. Two BREATHS every 15 seconds.

PROCEED to STEP 4 – CIRCULATION

In my opinion every pet owner should be comfortable with basic dog and cat First Aid. 

It's the responsible thing to do- and you WILL need it at some point.

You need to practice.

Get up to speed on ALL the common dog and cat emergencies with