If you’ve looked at different kinds of street photography, street photography that awes, finding an subject/object in that image that contains another image for the background is not an uncommon occurrence.
To get a good image in the background be aware of any large ones around you–posters, murals, billboards, graffiti, and the like. When you spot a giant image you like and that a subject/object would fit well into (a person, dog, etc…) or almost fit into (doesn’t have to be exact), stand some distance in front of it and wait for an appropriate subject/object to pass by.
When the image and passing subject/object meet, start snapping and keep snapping until the subject passes the image. One of the photos is bound to be compelling.
In order to do this, have your camera set so that the shutter opens and closes as fast as you can get to without it being too underexposed and start snapping. Consider Av mode with a wider aperture (say, f/5) and a high ISO (say, 800).
I prefer using Tv mode (S mode on a Nikon) and a shutter speed anywhere from 1/200 sec to 1/2000 depending upon the light cast upon the image you are using for a background.