Depth of Field: There will be math.
Most of us learned that one increases depth of field in a photograph by stopping down, which is the same thing as increasing the aperture of a lens. (This is one, but not the only bit of confusing terminology in photography.) That's the simple part. Actual depth of field is a function of the focal length of a lens and the lens diameter.
Focal length? Focal length is all about converging light on the plane of "film," or usually sensor. To simplify, focal length is the distance from the optical center of the lens to the point on the sensor where that light converges. If one thinks of the light from a given scene shaping into a pyramid as it converges in the aperture of the lens, and then is projected onto a sensor, it's not too hard to visualize that a long lens will narrow the field of view (the amount seen of the scene). Long focal length = narrow field of view.
For example, a 500mm lens will have a field of view that is tiny compared to a 20mm lens. That's why the 20mm is called a "wide angle lens." That angle is the field of view.
Lens diameter above really refers to the diameter of the "pupil" through which light passes. F8 in a 25mm lens produces a pupil that is much smaller than that produced by a 500mm lens at f8. The trick is that both of the f8 settings will result in the same light on the sensor. That's because in the long lens that light travels far longer than in the short lens, and with that travel, the light's intensity decreases (actually, it decreases by the square of the distance). The light is the same as far as the sensor is concerned. The fields of view are much different.
Which brings us back to depth of field...depth of field is proportional to the aperture (f stop), the subject distance², the circle of confusion and inversely proportional to the focal length². Circle of confusion? Circle of confusion refers to the size of the sharp area projected on each pixel, or the largest blurred area that we can still see as sharp. Why is the sharp part called confusion? We're now getting back to at least the early 1800's, and it just may not be worth going there for this discussion.
What is worth considering is that for any given focal length, the smaller the aperture (the larger the f #), the greater the depth of field. The farther away the subject of focus, the larger the depth of field. The longer the focal length, there is a major decrease in depth of field (as the denominator above is squared).
So, from a practical standpoint, if I want the greatest depth of field, I use the widest angle lens available, and I focus on something that is not close to me. OK, that sounds simple enough, but it is not quite that simple. How could anything that involves a circle of confusion be simple?
Older lenses came with depth of field scales on their barrels, but this isn't the case with newer lenses made for digital cameras. Many DOF charts are available online, as are calculators, but the easiest approach may be to download an app that is a DOF calculator (simpleDOF is even free).
There is one more thing. Diffraction. Too much effort towards maximum depth of field, can lead to blurry images. This will be discussed as it's own topic in the near future. Nikon discusses it here for the new D800: http://www.nikonusa.com/en_US/o/Y6wrkA9OU_z04IreazIXl_22UII/PDF/D800_TechnicalGuide_En.pdf