I am not an avid wildlife photographer by any means, but it does give me a certain amount of buzz when I find the opportunity to capture it on film or digital media, as most of my work now is.  For me, living where I do, most of the wild creatures I have contact with will be at wildlife centres and zoos! Even so, these places do provide an opportunity for those of us who can’t readily find it in the true wild to whet our appetites for it.  I found that using a long lens, (in my case a 70-200 with image stabilisation), to be best for this kind of situation.  At least you can get past the wire mesh of fencing with it.  Using a good stout lens hood is always an essential for pressing close to glass screens to avoid reflection.  Also, demonstrations with wild birds, like the Eagle Owl and other birds of prey allow some good opportunity to get in close.  Give it a go for yourselves and enjoy.