That's a pretty broad question that leads into a large number of branches of pattern recognition and general machine learning techniques. There's not a simple a

That's a pretty broad question that leads into a large number of branches of pattern recognition and general machine learning techniques. There's not a simple answer and no single algorithm is going to work well for all 'animal sounds'. I'd recommend picking a particular animal and perhaps a particular call that you're interested in and searching through the literature to see what techniques are currently in use.