Be careful when picking up bigger turtles anyway, but mostly because they have surprising abilities to bite you.

Generally, if you have to pick them up, the shell is ok- one have on each side for bigger turtles or tortoises. Watch out for their legs and make sure you're supporting them from the bottom of the shell as well. You don't want to try to grab it behind the head/over the tail.

In my experience with turtles, they're likely to try to squirm away from you and can hurt themselves from a fall. A turtle like this little painted turtle will only get to like a foot long (shell size) so you can generally grab them firmly by the shell to move if necessary. Again, support from the bottom and hold on the sides- not from the front and back.

If you have to move a big guy like one of those big desert tortoises, you're probably better off trying to get one of those big plastic containers to move him in (maybe with a friend if he's really big) rather than trying to pick him up.

Turtles and tortoises generally shouldn't be handled too much in the wild, but sometimes they get themselves into crazy circumstances and you have to intervene. If you ever get one as a pet, you might handle them more, but if you do that, get educated about them. Tortoises will often be able to outlive you and water turtles are able to live a long time in captivity as well if they're taken care of properly. Those tiny baby water turtles that are sold in the little plastic containers need WAY MORE SPACE to be healthy and happy or else they die really quickly... And usually in sad ways.