Most of the hidden pictures I have been drawing are for the "Gaby's Journal" feature, in which Gaby and her family travel the United States, seeing all kinds of historic buildings, museums, national landmarks and parks. This time it was the dinosaur exhibit at the Smithsonian in Washington D.C.
Since these illustrations are based on real places, I usually start out by collecting a bunch of photo reference. The internet makes this extremely easy! I usually find some general "official" photos on Google Image Search and then try to find some more personal first-person photos on Flickr. I've even found some 3D models in the Google SketchUp 3D Warehouse so that I can position a building just how I want.
My next step is to mash up all this reference in photoshop to work out the composition of my drawing. Since illustration does not have to perfectly mirror the real world, I can grab one element from a photo that I like and flip it, or draw on top of it to extend it, and then drop other photos in the background or foreground, etc. etc. etc. Here is an example that I made for this illustration, which uses three or four photos and a lot of digital drawing.
I decided I didn't like that one very much, so I made a second composition, which I ended up using instead. Once I settle on the composition, I print this out and lightbox the general shapes onto my bristol board. Then I can finesse the drawing, and make everything look consistent. This digital "comp" technique saves me a lot of time, so that I'm not trying to figure out all of the perspective and angles of things from scratch.
The last step, of course, is to add the hidden objects! ;)