How to install?

Installation steps are standard. In Blender User Preferences > Add-ons, click Install Add-on from File...

Then browse to the angle_tool.zip file that you downloaded and install it. Then enable it.

How to add shortcut?

Go to Blender User Preferences > Input, and under 3D View > Mesh (Global) add a new hotkey with the name mesh.angle_tool so that your entry looks something like this:

If you are using the legacy version of the tool, called Corner Extrude, then please enter mesh.corner_extrude instead. Then either use the shortcut or look for Corner Extrude in the Search Menu.

How to use?

Use hotkey or look for the Angle Tool in Search menu or the Face drop-down menu in Edit Mode. Or use the button in the Toolshelf on the left of 3D view.

The command is designed to be used with a cross-section of your mesh, i.e. flat geometry, but I'd be interested to see if you can find other uses for it. So in Edit Mode select some geometry - can be Verts, Faces or Edges. After that switch to Edge Mode and select one Active Edge. The Active Edge will act as a hinge for the other selected geometry to extrude and rotate around.

What if my mesh doesn't have an edge that is suitable as a rotation pivot?

In some cases you have to create a temporary edge by extruding out a vertex at the desired angle. This can then be used as the Active Edge for the Angle Tool to pivot around. Afterwards just delete the vertex and the floating edge will be removed. Here's an example of what that might look like:

Why is the resulting geometry looking uneven or squashed?

Please check the scale of the object and make sure it is uniform. Angle Tool is currently affected by the Non-Uniform Scale ratio of the object. This will be fixed in the next version. In order to get a perfect result, please Apply the Scale of your object to its data.