Zoo's are a great place to get started in learning how to photograph birds but you must always keep in mind those distracting backgrounds.. When visiting a zoo to photograph birds, try, when possible, to wait until feeding time and then try to position yourself to get the clearest view of the bird as possible and at the same time getting as clean as background as you can. Once you are in the best position you can, your next obstacle you need to consider is if there is any fencing or glass obstructing your view.
If their is some type of fencing or glass in front of you place the front of your lens as close and as square to the fence or glass as possible. In the case of wire or mesh fencing, point it through the center of the opening and set your lens to its widest aperture. This will help to blur out the wire or mesh. If on the other hand you are lucky enough not to have any fencing or mesh in your way then get a basic composition and then check your background for any distractions. The idea is too keep it as clean as possible with the least amount of clutter.
For birds with indentity tags or rings, try setting a wide aperture and include out of focus foreground detail to obscure the ring or identity tag. Also try to crop in tight on your subject to create a bird portrait. This is great and easy of way removing distracting clutter and backgrounds.