How do I create a nice miter joint between these two pieces? I would like these two pieces to meet up at the correct angle so there is no overlap and no distance between them. I'm used to sketchup where I would have been able to use the snap to intersection functionality to drag the edge lines to the point where the pieces intersect. It doesn't seem like blender has snap to intersection functionality. What's an easy way to accomplish what I'm trying to do?
As always, I'm open to correction, but creating miters at the ends of existing meshes is a fuss in Blender, unless the angle is at 45 degrees, and you can KC cut through with constraints, or ShiftCtrlAltS shear the ends of the stock pieces to a known extent. The shipped 'TinyCad' add-on can help, generating vertices at the intersections of edges, but even then, you'll find yourself creating guides of one sort or another to snap to, removing and creating faces by hand.

By far the quickest way to create miters is with polygonal curves. Create a track and a profile curve (possibly by AltC converting them from duplicated edges borrowed from existing meshes) 


The profile curve will be swept along its local Z
Its origin will lie on the track curve
Set the track curve to 2D in its data tab, fill 'None'
Set the Bevel Object of the track curve to the profile curve..




...and miters will be formed at every corner. The rightmost object has beeen converted back to a mesh; you may have to hit CtrlN in Edit mode to make its normals consistent.