Most places just want you to have a true love of animals and a passion to help them have better lives. However, you should also be dependable, with few or no sick days, especially if you'd be the only one there at that time, because you are responsible for all the animals, and if you don't show up or can't get anyone to cover you, they go without food, water, and must live in their own filth. You should also be able to work quickly, thoroughly and efficiently, and be able to lift up to fifty pounds. It's also a plus if you have experience with animals, either personally or professionally, and know how to spot changes in animal behavior, whether or not the animal is aggressive, afraid, friendly, etc., and how to keep yourself and others safe by properly handling the animal, although most places are usually willing to teach you this.
Also, please don't go in expecting this job to be all playing with the animals, with little or no work. It's actually the other way around. You don't get a whole lot of interaction with the animals, and most of it is cleaning up after them, and providing them with food and water. If you want a place where you get more interaction with the animals, try an animal daycare.