Having recently overcome various difficulties to successfully drape an image over a surface in Civil 3D, it may be useful to pass on a few points I have learned. There are various posts and videos out there that helpfully go through this process, but some of them (including Autodesk sources) contain information that is irrelevant or just plain wrong, and none of them contained all  of the information I needed to complete the task.

I used Civil 3D 2015 for this, but the principles apply to all recent releases. Here is the basic sequence required:

1. In the drawing containing the surface, attach the image to your drawing using your preferred method (ImageAttach, Xref, ClassicImage). I’ll assume you’re familiar with what you need to do to get the image correctly scaled and aligned with the surface.
2. Invoke the DrapeImage command, which will show you this dialog:
   Make sure this is set for the image you want to drape and the surface you want it draped over. You can change the Render Material Name to whatever you like, or leave it as the default. Pick OK.
3. You no longer need the image attached to the drawing and it will probably only confuse matters, so you can use use the Xref or ClassicImage command to detach it.

If you’re really lucky, that’s it. You will have a lovely-looking surface with a draped image over it. However, at this stage that’s pretty unlikely. Don’t panic! You also need to ensure the following conditions are in place:

1. The surface will need to use a surface style that includes triangulated surfaces so the image has something to drape over. In the Toolspace, under Surfaces, right-click on the surface and pick Surface Properties…, then change Surface Style to anything with triangles, triangulation or TIN in the name (this varies depending on the template used). If you don’t have such a style available, you’ll need to make your own or edit an existing one using the button with a pencil in it.
2. While you’re in the Surface Properties dialog, have a look at Render Material. That should be showing the Render Material Name you specified in step 2 above. If it isn’t, make sure it is. Pick OK.
   Bonus tip: if you later need to remove the draped image from the surface, you can do so by changing the Render Material to something else (e.g. ByLayer).
3. Still seeing nothing useful? Make sure you are using the Realistic visual style. You can get at the Visual Styles Manager using the VisualStyles command, but in recent releases it has been made easier to switch visual styles using the in-canvas control:
4. Still nothing? Try turning off Hardware Acceleration. Right-click on that glowing blue blob thing in the lower right corner and pick Graphics Performance…That will give you a dialog with a Hardware Acceleration switch. Turn it off, pick OK and (hopefully) voila!

Note that the above conditions need to be in place when plotting, too. You might not expect hardware acceleration to make a difference to plotting, but in this case, it does.