I found Traces of Hecke operators by Knightly and Li very readable. They threat Gl(2,R) by a similar method. Knapp or Wallach is also nice to read and more general. They have chapters for Sl(2,R) and Sl(2,C), Bumps Automorphic forms as well but is closer to Knightly-Li.
The main ingredient are the intertwiner. At their poles and zeros you find the discrete series inside non-unitarizable representations.
Ruling out unitarizability is often achieved by studying the growth of the matrix coefficients.