I want to round out this right angle join between two edges. How can I achieve this effect in red?
Next with the two vertices selected snap the cursor to them (Shift+S-->Cursor to Selected). Change the pivot point type to 3D Cursor and enable snapping tool (Vertex). Select the bottom vertex, snap the cursor to it and (being in side view) press the Spin button (set the steps number in a Tool Shelf as you like). Next select the vertices of the arc, rotate and scale it to make the joint.
Select the vertex which creates the straight angle, press Shift+Ctrl+B and set the arc's size. Enable snapping tool (Vertex). Extrude the bottom vertex and snap it to the other one as pictured below. Snap the cursor to it (with 3D Cursor pivot point type), then delete it. Select the diagonal edge, subdivide it (W-->Subdivide) and set the subdivisions number in a Tool Shelf. Next press Shift+Alt+S,1. Finally translate the arc along Y and Z axes to snap it to the other vertices.