Finding the age of a living thing. like a human being?

There won't be any method of finding an exact age right down to the date of birth. It's unlikely, anyway.

There are ways, however, to get a more general idea. Appearance, as simple as it seems, is very effective. If you know what you look for you can get someone's age down to within a few years with complete confidence, and even if you're not very good at it you're highly unlikely to be off by more than a decade.

A more scientific way could be a genetic analysis. Our somatic cells (body cells, not gametes) lose DNA every time they replicate and normally that DNA isn't replaced. The level of DNA degradation could give a good idea of age.

Bones would help, too. Our bones change throughout life; in children, a large amount of bones are cartilaginous and what would be considered a bone in an adult might be a collection of bones in a child. As we age, our bones also alter. Sometimes cartilage starts to become like bone, the bones themselves will be weaker, and so on.

Of course, the way you do this will all vary from species to species (and from gender to gender, even).

Carbon dating is only reliable for organic matter that has been dead for a few thousand years, so it does not apply to living things.

Teeth are a good measure of age for humans too. The degree of calcification in some bones can be used also. These methods are generally used on the remains of dead people (in archeology and forensic science) but can in theory be observed on the living with a radiography.

The estimate of age can be very precise for babies (within a few weeks or months from the actual date) but gets more and more uncertain for older people.

cats i know vets tell by their teeth or something, when you get your cat fixed, in the paperwork you get back it shows a birthdate..well, it's estimated birthdate, but my one cat, i know his exact birthdate because my moms cat had him..and the estimated date was only off by a week or so, i would imagine it works the same with dogs..humans they have ways of telling but i think it's more complicated and less exact