Right adjoint of pullback functor

Question

Let $f:A {\rightarrow} B$ be an arrow in a topos $\mathbb{C}.$ The pullback functor $f^*: \mathbb{C} /B {\rightarrow} \mathbb{C} /A$ sends an object of the slice category $\mathbb{C} /B$ to the pullback of it along $f$. The fundamental theorem of topos theory (Theorem 17.4 in McLarty), says $f^*$ has a right adjoint $\Pi _f: \mathbb{C} /A {\rightarrow} \mathbb{C} /B$. My questions are:

1. How does $\Pi _f$ work on objects ?
2. How is the natural isomorphism $\text{Hom}_{\mathbb{C}/A}\left(f^* Y , X \right) \simeq \text{Hom}_{\mathbb{C}/B}\left(Y , \Pi _f X \right)$ defined ?