I agree with @kimball's suggestions. The first thing to do is to get a handle on what it looks like for GL(2), then upgrade to general $G$ only as needed. For a basic introductory references, starting with Knapp's Theoretical Aspects of the Trace Formula for GL(2) and Gelbart's Lectures on the Arthur–Selberg Trace Formula. Then depending on your needs, I find Arthur's own An Introduction to the Trace Formula (MSNAn Introduction to the Trace Formula) an excellent guide to his own work for the general case.