  We discuss the Bousfield localization $L_E X$ for any spectrum $E$ and any
$HR$-module $X$, where $R$ is a ring with unit. Due to the splitting property
of $HR$-modules, it is enough to study the localization of Eilenberg-Mac Lane
spectra. Using general results about stable $f$-localizations, we give a method
to compute the localization of an Eilenberg-Mac Lane spectrum $L_E HG$ for any
spectrum $E$ and any abelian group $G$. We describe $L_E HG$ explicitly when
$G$ is one of the following: finitely generated abelian groups, $p$-adic
integers, Pr\"ufer groups, and subrings of the rationals. The results depend
basically on the $E$-acyclicity patterns of the spectrum $H\Q$ and the spectrum
$H\Z/p$ for each prime $p$.
