The question strikes me as too vague (what is that paper you're reading, by the way?). Like others, I'm assuming the subject is finite groups, rather than algebraic groups or quantum groups or something connected with modular forms. Usually the modular theory of finite groups is approached via the classical Frobenius-Schur theory, which is especially slanted toward characters but can be recast in terms of the Wedderburn structure theory of group algebras. Modular theory allows for a wide variety of approaches, including the narrow but fruitful one in Alperin's book. Serre's concise book starts out in a fairly elementary style (for an audience of chemists), but by the third part on modular representations the sophistication has escalated a lot. It's an important short treatment but scary for newcomers.
There's a lot to be said for the somewhat old-fashioned, concrete approach taken in the original Curtis & Reiner book Representations of Finite Groups and Associative Algebras, toward the end of the book. It does presuppose some of the earlier material, slanted toward ring theory rather than characters.
For a really short and relatively elementary expository treatment of both "ordinary" (characteristic 0) and modular representation theory, motivated by a single family of almost-simple groups, there's an old paper of mine in American Mathematican Monthly (1975), "Representations of `$SL(2,p)$".
The bottom line is that you need to focus on which specific area of representation theory is essential for your needs. It's a very big subject.