Here are some rules on picking up a cat from both a common sense and medical standpoint. Firstly, we should ask whether we are picking up our cat because we want to or because we need to. In general cats who know us don't mind being picked up and many will like it once they are settled in your arms or on your shoulder although cats tend to have a time limit on how long they like to be held. The time limit can be quite short. We should be sensitive to the time limit.
It is probably fair to say that we should not pick up our cat to please ourselves too much or for too long. We should not automatically presume that cats like to be picked up and held by us. Cats don't naturally have that desire in my opinion. It is more natural for people to pick things up and hold them or cuddle them. Often, therefore, the motivation to pick up a cat comes from us and on that basis we should make sure our cat likes it or tolerates it well.
We should be able to read a cat's demeanour to assess whether he or she is in the mood to be picked up. This leads to the question whether your cat has a character that is predisposed to being picked up. Some cats like it, some don't and some are in the middle. You have to figure out where your cat is in that range.
Note: feral and/or stray cats should not be grabbed and picked up. The cat does not know you and will be defensive. You are likely to get scratched and then some people will probably blame the cat. It would be wrong to blame the cat. We must remember that we are many times larger than a domestic cat. We can be intimidating just by our presence, which can prompt defensive behavior in the cat.
When picking up your cat, the underlying principle is to make sure that he or she is well supported when you do it. That is obvious but children or inexperienced cat caretakers tend to grab a cat in both hands at the shoulders and lift. This leaves the rest of the body hanging down. That puts strain on the cat's body and in fact makes it harder for the person to hold on to the cat anyway. The best way is to place one hand under the cat's chest and the other under the cats body near to the hind legs and lift. Then the cat can be placed on your shoulder or in a more vertical position near your body. However, cats like to remain in a natural, upright position. We should cooperate in that desire. Sometimes people cradle a cat like a baby, with the cat's belly pointing upwards. This is incorrect. It is the person thinking that a cat is a baby. A cat will not like this position and may wriggle and become defensive. Some cats may accept it but nonetheless it is not sensible to do it.
Always comply with the cat's preferences and desires. Don't force your cat to do things to please yourself. It won't work and will make your cat stressed and distant from you emotionally.
If you have to pick up a cat and the cat is apprehensive you can pick him up by the scruff of the neck provided the rest of the body is supported and the cat is not overweight. The cat will go into kitten-mode and relax as if being carried by his mother. It should be done with care. Although this may not happen for older cats.
If you are picking up your cat to give medicine such as a pill (I advise using a pill-gun) I have found that a good technique is to use a towel. Cats don't like being given pills. They might try and force your hands away and might scratch you inadvertently. I place the folded towel on a flat surface at counter height and lift my cat to the towel. Gently push him onto his belly and then wrap the towel around him ensuring that the forelegs are inside the towel. It takes a bit of practice and some cats will be very resistant. But once achieved it is much easier to deliver the pill as you have control.
An alternative to the towel is a special cat bag which zips up around the cat leaving the head outside. I have not used these and cats will in general dislike them, I suspect.
If delivering a pill, it can be useful to have an assistant as she can help to reassure the cat and keep him still while you administer the pill.
Never wrestle with your cat when picking him up for whatever reason. You'll lose that battle and make things worse for the next time. Cats will remember bad experiences and become defensive. It is better to tease and trick a cat into doing something. We should be smarter than them. Although sometimes I doubt that.
Finally, the completion of the process should be gentle! Your cat should be placed on the ground carefully and on all fours.
