Slippery When Wet

Working with reptiles, one of the skills that I first had to develop was the ability to safely handle animals.  It required me to work on my awful hand-eye coordination for quickly grabbing cranky snakes and lizards, knowing how to strike a balance between being firm and being gentle, and counting my fingers at the beginning and end of each day to make sure that the count stayed the same.  Learning to handle our amphibians was much easier.  There was really just one rule:

Avoid, if possible.

Frogs, toads, salamanders, and caecilians have (for the most part) moist, permeable skin compared to the scaly hides of lizards, snakes, and crocodilians.  It's delicate and can easily be damaged.  Furthermore, their skin is absorbent, so whatever you have on your hands can seep into their skin, causing health problems.  This is one of the reasons why amphibians are so susceptible to pollution and contaminants in their environment compared to other animals.   Also, they tend to be so tiny compared to many reptiles - it can be so easy to unintentionally harm them, to say nothing of stress.  As such, it's better to avoid handling them if you can.  If you need to move them, it works best to gently shoo them into a smaller container and carry them in that.

When you do need to handle them, you can use gloves (especially helpful for poison dart frogs and other species - even though zoo-bred/zoo-fed specimens aren't nearly as toxic as wild ones, they can still have something of a kick).  Gloves, however, can reduce your dexterity and make handling difficult.  If you do it bare handed, make sure your hands are clean, but don't have any trace soap or chemical or sanitizer on them.  Then, make sure they are wet, preferably with reverse osmosis water.  Most zoos with amphibian collections have an RO filter on the water supply for their frogs.  Keeping your hands wet reduces the risk of accidentally tearing the skin.

Of course, holding a wet frog in wet hands makes them even slipperier and harder to handle than normal, which can increase the risk of dropping them or having them jump out of your hands.  Which is why I again refer you to rule one of handling amphibians: avoid, if possible.