Unfortunately, it is very difficult to find out an adult cat's exact age.
It's easier if they're still kittens. You know if they have their eyes and ears closed that they're under 1-2 weeks of age, that if they have open, blue eyes they're between 2 and 6 weeks of age, that if they have their premolars but no other teeth that they're around 4 weeks of age. You can also estimate based on their size.
Once a cat is an adult, you can really just guess the range based on their health. An adult cat who is overall healthy, fairly active, not suffering from arthritis and probably not missing teeth, you can guess the cat is between 1 and 6 years of age. If the cat is more mature, but still fairly healthy, probably somewhere around 5 to 8 years of age. If the cat is suffering arthritis, they are likely a senior.