For some reason I am unable to pick our cats up so they are comfortable and hence they always struggle and start scratching when I pick them up. Walnut - our British Blue Shorthair - does not like being picked up at all regardless of who it is, she is much happier just being stroked whilst laying down. Dougal doesn't care what you do to him so I can pick him up still laying flat out on his back or side. Treacle is still a bit fidgety when I pick her up so she doesn't like it.
Generally cats enjoy being held for brief periods but they do like to be in control of their own movements and will usually only feel at ease in the arms of a human they know and trust.
To pick up a cat you must first gain the cat's confidence and once it is relaxed pick it up supporting its hindquarters. Lift the cat in as natural a position as possible talking to it to reassure it. Use one arm to support the cat's hindquarters and the other for support and stroking. If the cat struggles then put it down and try again later - do not force it to be picked up.
Children tend to be a bit rough with cats - particularly kittens - so show them how to stroke and handle the cat and do not let very young children pick cats up as they do not understand how to hold them.
Cats love to be stroked or rubbed around the ears and chest, neck and back but do not stroke a cat's abdomen and back legs as they tend not to like it.