MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

Another standard reference for the Plancherel formula is the book: $SL_2(\mathbb{R})$, Addison-Wesley, 1974; of course $SL$ stands for Serge Lang.
The Plancherel formula and the Selberg trace formula have in common that a trace is computed in two ways. But they deal with different representations of $G$. For $G$ a suitable locally compact group (type I, unimodular, separable), and $f\in C_c(G)$, the Plancherel formula is $f(e)=\int_{\hat{G}}Tr\pi(f)\;d\mu(\pi)$, where $\mu$ is the Plancherel measure on the dual $\hat{G}$; and the difficulty is, in concrete examples, to describe $\hat{G}$ and $\mu$ explicitly (or at least to describe explicitly the support of $\mu$, called the tempered dual).
Another standard reference for the Plancherel formula is the book: $SL_2(\mathbb{R})$, Addison-Wesley, 1974; of course $SL$ stands for Serge Lang.