Well, they will typically let you know by dropping alot of food when eating, or not finishing their food.
And while being ridden, they will grind their teeth. When you apply pressure on the bit they might toss their head, flatten ears, or full out refuse to do anything. I've seen one horse with an abcess in the mouth buck and rear when being ridden.
Mine was tossing his head and throwing fits while wearing a bit. Also dropping grain. Got the vet to check him out.. I guess that's how to know for sure. He drugged him, cranked his mouth open, and let me feel his teeth before and after the float. I had my hand in there all the way up to his eyeball :) Posted via Mobile Device
If it's been more than a couple years since the teeth were done and the head tossing is a recent development, odds are there are some some sharp edges in there causing pain. Getting teeth floated yearly is pretty common, though some horses will need it done more or less frequently.
If the teeth check out OK, have the vet also look at eyes and ears, and if all those are OK, then re-evaluate bit type and size.