How does aperture affect depth of field?

The aperture  setting, or opening of  the lens has an affect on the depth of field. Regardless of the format of the camera or the focal length of the lens , as the aperture is changed, the depth of field alters.

A large aperture opening of f 2 (as in the top diagram) produces less depth of field in an image while  smaller opening (as in the lower diagram) f 16 produces more depth of field in the image.

Here the point of focus has not been moved - but as aperture is stopped down more aspects of the tree come into focus. Look how limited depth of field can be use to separate the foreground from the background as in the image on the left.

Note that there is less depth of field closer to the camera position from the point of focus than in the distance. As a general rule, remember to allow for this by focusing on a point closer than mid way, about 1/3  from the closest object you want in focus. The remaining  2/3 of the area in apparent sharp focus will relate to the objects further away from the point of focus.

f/stop - The smallest diaphragm openings produce the greatest relative DOF however the image sharpness is actually less than a moderate opening produces because of diffraction or bending of the light rays. Light rays which closely pass an edge bend toward the edge as they go by much like when you touch the side of the stream of water falling from a tap (try it). The stream (or a portion of it) will bend toward your finger. The rays thus scattered are then out of focus. Diffraction occurs at any lens opening but since the proportion of diffracted rays to non-diffracted rays is greater with very small openings than with larger openings, the image sharpness is slightly less at the smaller openings. The faucet experiment works to show this effect too. Open the tap to the smallest steady stream you can and lightly touch the side of the stream with your finger. Chances are the entire stream will be diverted toward your finger. Now open the tap further. As the volume of the stream increases, less of it touches your finger and more of it falls straight.

Lens quality - Aside from actual differences in the quality of lenses, no lens is equally sharp at all the available diaphragm openings. The maximum sharpness of a lens is obtained in the middle range of the available f/stops. For example, if you have a 50mm lens with a range of f/2 to f/16, your lens is probably sharpest when used at f/5.6 or f/8. This is because of the limits of lens design. Maybe someday we'll figure out how to design a lens that is equally sharp at all openings but we are not there yet. In the meantime lens designers go for the greatest sharpness in the middle range and compromise on the rest. Although not a lens you should consider your filters as part of the lens. Buy the very highest quality you can afford. They are in the light path and your image will be only as good as can be produced by the lowest quality piece of glass (resin, plastic or gelatin) in the light path. It should be obvious that you must keep all your lenses and filters clean.

Two other factors play a part in depth of field:
subject distance
focal length

Want to learn more? - do a workshop or one on one with Lloyd Godman