Use this little guy to align an object of a face, or an edge, etc, to the normal of another object.

First, have either and object or sub-object [like a face] selected that you want to align to a face of another object.

Activate the mode …

Cursor will look like this:

The cursor changes to this when you are over a face that can be the source align:

When you click DOWN on the face, a little blue arrow of the normal appears:

Lift up on the mouse button, and the cursor changes back to

Then, click over a face to align TO … this will be indicated by the same cursor:

If you move around to different faces, you can see the green normal line move:

Choose a face to align TO and blam, they line up.

You can then position on the axes, extrude, etc., as needed.