It depends on the kitten, some really object to being picked up and it does take some time for them to trust you enough to at least tolerate the idea... and you need to slowly work up to holding... start with just picking up (with as little fuss as possible) and immediately put back down. Repeat that many times a day until it means nothing to the kitten, then try holding for a second or two and putting down...they learn that yes you are restraining them but not for long and it doesn't worry them as much.
For clipping claws though, you really want them still so you don't accidentally cut too close and hurt them... so see if your kitten still has the "scruff reflex", this is when you take a scruff of fur behind their neck... this is how mama cat picks them up so they often have the reflex of going limp and relaxing. This can help you hold them still for their nail clipping...