The most important thing you can do is make sure to wash your hands thoroughly between each animal you handle and before you head home. You should also bring a pair of rubber boots or old shoes that you don’t normally wear so that you can wear those around the shelter instead of tracking any possible bacteria, viruses, or fecal residue from any of the shelter animals back to your home. That’s the key way to prevent bringing disease to your pets. If you handle the quarantine ward, make sure they have a pan with bleach outside the door so you can step in it with your rubber boots to get rid of any possible diseases before you continue through the other animals you may handle.
Handling wise, make sure to look for body language so you don’t get hurt. This is mainly for cats and dogs. Make sure to try and appear as unthreatening as you can. Especially in the case of fearful animals. Body language is very important and you must make sure you aren’t accidentally displaying threatening behavior to the animals. (Like towering over them or reaching towards their blind spots).
If you are just socializing animals, like rabbits, let them come to you at their own time. Rabbits are prey animals and some are very shy. If you need to pick a rabbit up I think you should pick it up much like you would a cat and make sure to have a firm enough hold that it doesn’t just hop out of your arms.
Im sure the shelter will give you a run through of how they run things, make sure to take notes!:3 hope this helps