Composition seemed to top the list, since overlapping shapes is such a powerful way to represent one being nearer than another.
Value is a relatively easy variable to adjust in order to create a significant difference between adjacent shapes. Remember that the range of values you use in one shape compared to another suggests its position within the illusory space. If a shape is made of a wide range of darks and lights it appears closer than one made of mostly middle values.
Color differences between shapes are also easy to create, and serve as a very effective way to make a convincing illusion of depth. The prevailing wisdom is that ( relatively) warm colors seem to advance and cool colors recede.
Edge quality may require more technical prowess than the other variables. Hard edges separate shapes while soft edges tend to connect them.
In the photo above, look at the figure on the left. The diagonal shadow above him seems to be perched right on his head. What might you change to make clearer where the figure and the shadow are relative to each other? Remember, it may take more than one variable to do the job.
Here I find the roof to be a distraction. I'd like to diminish its influence on the space. Could it be pushed farther back, or somehow made less assertive?
There are a couple of problems with this photo, above. The shadows on the building to the right are so black they look like holes in the wall, especially the one on top. I also want to untangle the telephone pole from the stuff behind it. While you're at it, could you turn down the dials on the whole group of buildings back beyond that car?
For homework, please take on one of these images and make a study to try out whatever adjustments occur to you. A study is meant to provide the answers to any lingering questions. It is not a painting, and it doesn't have to be a handsome product to do its job well. If your ideas are revealed to be less than satisfactory, then the study has succeeded in providing information that you need.