There's no fixed age for trimming a cat's nails. You can trim them when they're long enough to hurt someone. However, be careful when trimming; be quick and avoid injuring the cat's skin.
Generally, owners can start trimming a kitten's nails when it starts scratching or after it turns two months old. If the kitten is too young, the quick on its nails is not very clear, and trimming can easily damage the quick, causing the kitten to bleed. 
When trimming a kitten's nails, be careful not to cut too short; only cut off about 1/3 of the nail, then file it smooth. Some cats are afraid of nail trimming, so try to appease them with treats beforehand to reduce resistance. Nail trimming will only go smoothly when the cat is docile enough.
