PROCEDURE
Put on your headlight. Put on latex gloves. Halter the horse in a loose fitting halter. Standing on the horse's left side, facing the horse, and using your left hand, with your right hand on the halter, lift the left side of the lip to evaluate the left canine teeth (in a male) and the incisor teeth, tongue, inter-dental space and bars. Slide around to the other side to see the right sided teeth and gums.
Now (carefully) stand in front of the horse. Use your right thumb to gently hook the corner of the mouth (cheek) and pull it to the side. Now, using your headlight, look at the outside edges of the first few upper teeth. Do the same thing on the opposite side.
If you stand in front of the horse, holding the left cheek piece of the halter in your left hand (only do this if you have feel and confidence), push your right thumb through the corner of the horse's left mouth and push the thumb into the roof of the mouth. Your horse will lift its head and open it's mouth and you can briefly see the molar rows.
When I perform an oral exam, I stand in front of the horse, holding the tongue off to the horse's right side with my left hand. I put my left thumb into the roof of the mouth to look at the molar rows on the horse's left side. I reverse my hands to evaluate the horse's right molar rows. I feel all the horse's teeth without a speculum, but this is dangerous and should only be done by your vet.
TIPS FOR SAFETY AND SUCCESS
To get your horse to easily open their mouth, slide the end of your thumb through the corner of the mouth, and push it gently into the roof of the mouth (think of hitch hiking). As soon as the horse opens its mouth, release. When you need to look in their mouth again later, it will be easier.
ALWAYS use a loose fitting halter. Never even try to open a horse's mouth when they are wearing a tight halter. If you try, they will resist. A snug halter comes tight around the jaw when the horse opens its mouth, applying pressure around the jaw and creating discomfort. The horse responds by resisting.
Be careful not to get your thumb between the rows of molars that start about 3 centimeters behind the corner of the mouth. Those teeth can crush or even amputate a finger.
Do not try to put your hands in a horse's mouth unless you are completely confident that you can do it without being bitten.
I talk about putting the thumb in the roof of the mouth. Even though the horse's mouth is closed, if you lift the lip, you will see there is a large space on the side of the mouth in which there are no teeth. This is called the inter-dental space. The lower part of this is the bar upon which the bit sits. You can insert your fingers in this area without fear of being bitten, but beware of being further back than the corner of the mouth. Occasionally a canine tooth is very sharp, so be careful of those too.
When you use a head light, turn it on pointed away from the horse, then slowly swing it over to the mouth.
Looking in a horse's mouth should not be a struggle. If it is a struggle for you, either you are not doing it correctly, or the horse has not learned the cues that you are giving. Either way, it is best to stop and get help.
Before I look in a horse's mouth, I like to rinse it out with water using a large dose syringe. To do this, gently push the tip of the dose syringe at a 45 degree angle into the corner of the mouth and back between the molar rows, and press the plunger forward.
NOTE: There is a very small possibility for you to contract the fatal disease rabies from a horse infected with this disease if their saliva comes into contact with a wound on your skin. This is why you SHOULD ALWAYS wear latex gloves when examining your horse's mouth.