What chemicals and minerals are needed for fossilization to occur in an animal?

There are many different possible chemical pathways for bones to be become mineralised, and lots of different minerals that the bones can end up as: for example, the theropod Kakuru is known only from a tibia which mineralised as the semi-precious gem opal. See http://en.wikipedia.org/wiki/Kakuru

More generally -- as so often with very broad questions like this -- Wikipedia is the best place to start. See http://en.wikipedia.org/wiki/Fossil#Fos … _processes and links therein.