An electronic stud finder, (at left, $10 or $15 at the hardware store), will locate studs behind the wall surface and let you know where placement is possible.  (I put a strip of masking tape on the wall and mark the edges of the studs with pencil.)  Check vertically within the denoted space as well, to locate any possible fire blocking.  A shrine must be placed at least 1" away from any stud in the wall to leave room for the gripping toggles.

Now you can hold the shrine up against the wall to find where it looks right.  When you have it where you want it, level it with a small spirit level held on the front step, hold the shrine firmly against the wall and trace the back on the wall with a pencil.

Cut out the profile with a wallboard saw, (photo at right).  To start the cut, put the saw tip somewhere on the profile line and hit it with the heel of your hand (or something else) and drive the blade in.  Cut along the line as closely as possible, making your cut perpendicular to the wall surface and barely removing your pencil line.  The right angle at the bottom of the profile requires that you start a new cut to keep your line crisp.  If you've left a bit of the pencil line, you may need to trim a bit more off.  (You can practice your cuts well inside of the profile to refine your technique.  Also, a small practice hole is easier to repair if you miss-step in the placement of the shrine.)