Preface: In my humble opinion, the only Beast worth putting experience towards is the Bird of Hurricane as you can put it on a general to get a higher chance at a Double Drop from a Boss. The rest fall far short of the Dragons you will unlock later and should not be somewhere you waste Gems, Gold, and Medals.
With that out of the way, there are 4 Beasts total.
Bird of Hurricane
Lord of Lava
They each buff a particular troop type and the buffs increase as you level them with Spiritual Beast Experience Books and as you "Smelt" them.
To unlock the Beast, you must first upgrade your Pasture to the respective level and then apply 300k Experience to them. Once you have done that you can "Activate" the Beast and it is yours forever. You utilize the Beast by assigning them to a General. You can change which General they are assigned to but there is an hour cooldown just like the Dragons.
Smelting the Beasts costs a considerable amount of Gold, Gems, and Medals that could be better utilized elsewhere. But here is what that screen looks like.