Unlike fish, axolotls do not have a sensitive, protective layer, so they can be handled. They are still very delicate, and should only be held or touched when necessary, such as moving them out of their tank, into a feeding container. You want to be very gentle, and grasp them ever so lightly, like you are holding a small bird or insect. You only have a short amount of time to grab and hold your axolotl, as they will freak out, and do their best to escape you. 

 

The best method is with two hands, to stop them slipping forward, but they can still slip backwards. If your axolotl is already freaking out, let it go and wait awhile. If it is already freaking out, you'll most likely drop it. Dropping axolotls is not fun.

 

Like shown below, you want to grab it with two hands, using fingers to gently separate it's legs, and get a thumb and finger at least in front of its legs. This stops them using their legs to propel themselves out of your hand so quickly.