Wildlife photography, as a genre, is an expensive hobby requiring fast and long glass. But, don't despair. There are ways us normal folk can play this game.
For example...set up a bird feeder and a blind. You can arrange things so you're close enough and the birds are in good light...and a 70-300 VR will do the trick for you very well.
Or opt for the really small wildlife (insects and such). You could get a Tamron or Sigma macro lens (90 mm or 105 mm, respectively) and a tripod, and go in search of the chitinous creatures.
Zoos and animal parks offer the photographer opportunities, as well, where the 70-300 would turn the trick.
Whatever your choice, one thing for sure...wildlife photography takes patience. All God's creatures seem to have one thing in common...they are elusive and camera shy!
Best wishes!