Cats often won't tell us something is wrong, they are particularly skilled at hiding their pain. This is a survival instinct as in the wild cats are both predators and prey. They don’t want to expose potential weaknesses to other predators and make themselves vulnerable. If a cat gets to the point of expressing behavior that is the result of obvious pain or discomfort, it's often an emergency situation.
A great way to set you and your cat up for success is to start slowly getting them used to touching all over, especially on some of their most sensitive areas like feet, ears, tail and mouths. You can teach them to give you a paw, which will help when trying to cut their nails. Get them used to human fingers in their mouths so you can easily brush their teeth.
Snout to tail check ups can be a great way to bond with your cat and keep a good check on their health.
To get started, gently pet their head, sniffing the ears and removing dirt and waxy debris with a soft cloth moistened with cat specific ear cleaner. If anything appears red, smells bad or if you notice pepper or coffee ground-like dirt, get to the vet. These could be signs of an infection, the presence of ear mites, and you may cause pain if you attempt to clean.
If eyes tear excessively, have a thick discharge or if the pet is rubbing them, clean with purified water. Also observe eyes for differences in pupil size, if one is larger, this could be a sign of major medical problems and prompt medical attention is needed.
Next up we move to the mouth, take a careful look inside. Gums should be a healthy pink (except for pets with dark pigment) with no odor coming from the mouth. An unpleasant scent could indicate gum disease, tooth decay or gastrointestinal problems. Sweetness or an acetone-like scent could signal diabetes, but only your veterinarian knows for sure! Pay attention to hydration by feeling for moistness in the gums. Dry or sticky means you should encourage water intake. Dehydration is serious, so if skin at the nape of the neck sticks together when gently lifted, eyes are sunken and/or constipation presents, get to veterinary care!
The rest of the exam is like a gentle message, looking for things that don't belong like bumps, tenderness or wounds. Look for signs of skin dryness, a good brushing can help stimulate oil glands. Now the best part, reward your pet with a few treats or some play time!
Other things to keep an eye on are weight changes, changes in typical movements or grooming or changes in eating, drinking or litter habits. For example, decreased or increased thirst can be an indicator of changes in kidney function, diabetes, or other medical issues and should be looked at. Changes in urination habits can mean issues with kidney function, diabetes or urinary blockages. Urination outside the litter box can mean a bladder infection.
See the attached PDF from Pet Sitters international for a more detailed description.