NOTES: Before you start, let's TURN ON your ANCHOR POINT SNAP, this will help you perfectly line up objects on your canvas. CLICK EDIT>PREFERENCES>SELECTION and ANCHOR DISPLAY. This will bring up your SNAP window. I would turn TOLERANCE= 1, OBJECT SELECTION BY PATH ONLY= OFF, SNAP TO POINT= ON, WITH PX=3. This will allow you to grab anchor points with your DIRECT SELECTION ARROW and SNAP them to other objects and anchor points.
Also before you begin, make sure your SMART GUIDES are turned on by clicking CTRL-U. This will allow you to see when shapes and anchor points line up on your canvas.