Placing image on uneven surface

You have to make a map for the Displacement map to work on.

You could either do this manually painting white and black strokes — black to make the shape bend down, and white to bend up.  Or you could use a copy of the background to fudge it and get you started.

I have copied the cliff, made it B&W and increased its contrast.

You then right click and Duplicate to a New Document, and save that as a .psd file.  We'll call it 'Cliff Map'

Note: It is uber important that backward compatability is set to Always in Preeferences > Files (I think).  It won't work otherwise.

Place your shape and use Free Transform to get the perspective about right

Select the shape layer and go Filter > Distort > Displace

It opens this dialog box. When you hit OK it will ask you to load a map, so find and select Cliff Map

This is actually my second go.  I decided to add Gaussian blur value 2.0 to the map and save it again

I have used a tiny bit of Puppet Warp and ended up with this

What I like to do is place two copies of the map layer above the displaced layer and clip them to it.

Set one to Multiply, and one to screen, and adjust opacity to suit.  This gives us some shading, but we lose some contrast.

So to finish off, I've combined the displaced shape and the two shading layers as a Smart Object.

I have clipped a curves layer to that SO and given it some contrast.

Last of all I have clipped a 50% grey layer set to Overlay, and used dodge and burn (or a low opacity black or white brush) to reinfoce shadows and highlights.  It took me much longer to type this than to do it, so you'll be able to make a way better job if you take more time over it.

Good luck.

Here's the clever bit.  Notice I made the shape layer a Smart Object.

This means you can double click Displace  which reopens the dialog box so you can adjust the values.

You can also fine tune the map and save it again, or Save As with a different name.