While it's not possible to determine the exact age of a cute and cuddly kitten, unless you have it's actual date of birth, there are several reliable methods that can be used to get a general age range.
Look at the kitten's eyes. Their eyes usually open around eight days old, but they can open as early as seven days and in some rare cases as late as 14 days old.
Watch for movement. Kittens generally begin attempting to crawl or stand upright and walk between 14 and 21 days of age.
Observe the kitten's behavior. After 21 days, the kitten should be able to distinguish between objects and will try to investigate sounds.
Check the gender of the kitten. The kitten's gender won't be apparent until after six weeks. The urination cavity of a male kitten will be rounder and further away from the anus than a female kitten.
Feel the kitten's teeth. After two months, the kitten should have all of its baby teeth and the permanent incisors will be pushing their way through the kitten's gums.