So, we've established escapes happen. We've explored the main reasons as to why they happen. The next, most important question is, "What do you do?"
Well, that all comes down to a lot of details, including one minor one - what animal escaped? It's not just a question of what species, but what sex, what age, and, in many cases, what individual.
Obviously, if a salamander escapes you look for it, find it, pick it up, and put it back where it belongs. If it's an elephant, you go immediately to HR, drop off your radio and keys, and then drive away as fast as you can, face burning with embarrassment the entire time. In other words, the appropriate response varies.
Just to be dramatic, we'll consider the escape of a large carnivore, like a big cat or bear. So here's what you do when the worst happens...
1.) Communicate... but not too much
In the case of an animal escape, communication is essential. The person who first becomes aware of the situation needs to convey information to the rest of the staff quickly and clearly. What animal is out, where it is, how it's acting, where it's going, how many are out, etc. Can you see how the animal got out (good to know, no sense herding an animal back in only for it to immediately pop back out the same way). Are there other animals in that enclosure? Make sure they are secure. That last thing you need is more escapees (actually, there are lots of other "last things" you need).
Most zoo staff communicate through radios, which have an inherent flaw. One person can hog an entire conversation, preventing anyone else from speaking. If you don't have anything relevant to say, be quiet. Keep your eyes and ears open and your finger off the "Talk" button.
Communication means communicating with more than just keepers. It means letting other staff know what the situation is. It means (depending on the seriousness of the problem and the risk of danger) notifying police and/or EMTs. And it means communicating with the only animals less predictable than those on the loose... the visitors.
2.) Protect the Public
There is no animal escape situation that cannot be made worse by panicking visitors. If the animal escape occurs before the zoo opens, the job is easy enough... just do not open until the situation is resolved. If there are visitors present when the escape occurs... well crud.
Try to minimize the visitor presence by removing them safely from the area. If they cannot be safely removed (because, let's say, a polar bear is roaming the zoo nearby) get them somewhere safe, inside buildings that can be closed down. Also secure non-animal staff, such as gift shop and concessions, as well as docents and volunteers.
As a matter of fact, this is where your non-animal staff are given their most important role. Have them help guests to safety and keep open lines of communication, all while removing themselves from a dangerous situation. Having them help take care of visitors let's you focus on your main issue.
3.) Eyes on the Prize
Find the animal. Quickly. Ideally, you should be able to maintain a visual on it the entire time it is out. Keep staff appraised as to where it is going and how it is behaving. If you loose sight of it, your job of recapture becomes much more difficult.
All of this assumes that you have seen the escaping animal and that you didn't come in one morning and *poof* the bear was gone when you got there. That's why you always do a morning check, so that a potential crisis can be identified before adding the variable of the public.
4.) Mobilize and Contain
Trained keeper and veterinary staff should be dispatched with equipment - dart guns, shotguns or rifles, snare pools, etc - needed to recapture the animal. What approach you take will depend on the animal and its state. Can it be lured back in with a favorite treat? Is there a keeper that it's especially close to that it will respond to and follow? Can a few keepers with shields, hoses, or fire extinguishers drive it back to where it belongs? The keepers are supposed to be the experts on these matters, and they should have the insight into their animals to at least have a theory of how the animal would respond and what will work best. Which usually is 5.)
The zoo gates should be closed and locked down to prevent the animal from leaving the grounds through that route, while at the same time preventing more humans from entering the scene. The exception may be if it is deemed safe to allow visitors to exit the zoo through that route. In this case, staff should man the gates, both to keep other people from entering the zoo as well as to close the gates if the situation changes and leaving them open is no longer deemed safe.
Meanwhile, the entire time, the gun team should be following a dangerous animal ready to intervene. The first choice is always, ideally, to dart the animal. If it poses a threat to human safety, however, or is about to escape a controlled environment (such as about to exit the zoo), the gun team may make the decision to euthanize the animal.
5.) A Way Home
Some humans assume that zoo animals are unhappy in their enclosures. To that way of thinking, an escape would be a liberation. The truth often is, however, that the animal views its enclosure as its home and the outside surroundings as threatening and chaotic. Virtually every animal escape I've encountered has ended the same way - for every dramatic chase and recapture, there have been nine times where the keepers simply left the animal with a clear path to get back to its enclosure and in it went.
The ideal end game is to get the animal safely contained, either having let it wandered back in or darting it and carrying it back. Only when the animal is secure should a stand-down be issued and things return to normal. By this point, everyone will probably have shot nerves, which can only be cured by closing the zoo and consuming copious amounts of alcohol, followed by sleep. Equally important to the response to the escape, however, is what happens next.