How can I speak to Animals?

I've come across a number of animals in my wanderings, and the game tells me that it seems as if this Yak or that Cat or some Bird has something to say to me, if only I could speak to animals!

It then teases me further by telling me that somewhere, there is someone, who can teach my great hero this unique and powerful skill.

So... who is it that can teach me? Where are they? How do I find them and convince them that I ought learn the tongues of beast and bird and fish and fowl?

In the levels that say "Baba Yaga" with a picture of a mossy house, you can find a cat named Bayun on a stump. Feed him some rations and he'll say he can help you.

When you find the witch's house, choose the top option and your character will call on Bayun to help you.

After the level when you're at the camp, Bayun will come and ask to join you.

If you say yes, he will teach you how to speak with animals.