You can see the ‘quick’ as a pink, living, area with a curved boundary before the claw becomes clear which is keratin, a dead, hard material.
Yes, kittens need their nails clipped so they can get used to it. This makes it much easier when they are adults. However, outdoor cats don’t need to have their claws trimmed as activity keeps them worn down to the correct length. They also need them in their natural state to defend themselves when necessary. There is a further qualifier to that statement because older outdoor cats become less active and perhaps arthritic. They’ll stay indoors more. You’ll need to trim their claws. It is particularly important to check the claws of elderly cats as they can grow into the paw pad. Therefore even kittens who’ll become indoor/outdoor cats need to get used to having their nails trimmed so do it for all kittens.
But do it with caution and care. It should a gentle and precise process. There are professional cat and dog nail files that you might prefer to clippers. You should squeeze the toe between your thumb and forefinger to extend the claw. Clip the clear part of the claw only. This is the section beyond the ‘quick’. The ‘quick is where there is a soft interior containing the blood vessels and nerves. You have to avoid this area with care.
There are two difficulties in trimming a cat’s claws (1) getting the cat’s cooperation and (2) cutting the claw in the correct place to avoid the quick. The former should happen if you trimmed the claws of your kitten. The latter is about precision which is made much easier when you cat cooperates.
If your cat’s claws are dark or it is hard to see the quick, trim the claw just beyond the point where it starts to curve downwards but don’t take risks and take blinds stabs at it. The better you get at it the faster and more assuredly you’ll do it which obviously makes it easier for your cat. If your cat becomes restless you can do one paw one day and the other the following day. Minismising fiddling around is important because cats don’t like their paws being handled.
If you do inadvertently cut the quick the claw will bleed and the cat will feel pain. Hold pressure over the claw with a cotton ball or something similar. The blood will clot.