Reference about direct image sheaf

Question

I was searching in Internet but I was not able to find a proper book/notes/etc. in which are carried out explicit computations with direct image sheaves. In particular I was interested in examples (computations) of the form:

1. What is $\pi_{*}\mathcal{O}_Y$, where $\pi:Y \rightarrow X$ is a finite morphism?
2. If there is a Galois cover $\pi: Y \rightarrow X$, how can we use the action of the Galois group $G$ in order to decompose $\pi_{*}\mathcal{O}_Y$?
3. How to compute explicitly $\pi_*\mathcal{F}$, where $\pi:Y \rightarrow X$ is a "nice" morphism and $\mathcal{F}$ is a "nice or famous" sheaf?

In particular any reference in which examples with coordinates and explicit calculations are carried out properly are much appreciated! Thanks in advance