representation theory - Computing Brauer characters of a finite group

I am studying character theory from the book "Character Theory of Finite Groups" by Martin Isaac. (I am not too familiar with valuations and algebraic number theory.)
In the last chapter on modular representation theory, Brauer characters, blocks, and defect groups are introduced.

My question is this: How do we find the irreducible Brauer characters and blocks, given a group and a prime?

For instance, let's say we have $p=3$ and the group $G = S_5$, the symmetric group.
An example of the precise calculation or method used to determine the characters would be very helpful. Thanks.