I actually NEVER touched the bugs. they totally creep me out! lol
I got the preschoolers to do it
I would take all of the branches out of the cage (we had a cage once they were big enough not to escape) an put them in a washing basket.
we then removed paper, cleaned tray and replaced paper.
If we needed to we then replaced the branches with newer ones and then the preschoolers either transferred the bugs bag by hand, or if it was just me, I just gently lifted the branch they were on and let them climb onto new leaves.
If you are trying to pick them up, let them climb onto you/stick/etc..rather than pulling, lifting them off branch, as they have a strong grip, and you don't want to hurt them - pull leg off etc..
we had to clean and change quite frequently as the children ALL liked to take turns at spraying the leaves with water for the bugs to drink - the paper etc.. got pretty soggy.