Skip to the last paragraph if you want to avoid the backgound.
As previously mentioned radiation fog, is formed when the air temperature drops to near the dew point temperature (e.g., 2 degrees C), causing the moisture in the air to condense into small, suspended water droplets – simply clouds at the surface. Often when cool/cold air overlies a warmer water body or moist surface, the winds are calm, or very light, fog will form.
For radiation fog, this occurs when the temperatures approach the daily minimum, typically in the early morning hours. The cooler air can be the result of overnight radiation cooling, a frontal passage, or overnight cold air drainage into valleys or over water bodies, among others.
It also is worthwhile to think about when the fog will “lift”, i.e., when you can expect the visibility to improve. And, is it is worthwhile to wait for your shot. Consider that the air is heated and cooled by contact with the earth’s surface. Cooling temperatures in the evening due to radiation cooling result in formation of an inversion near the surface, i.e., the air near the surface is cooler than is the air above. Cooler air is denser than the overlying air and thus wants to remain where it is (vertically) – not buoyant. However, as the sun rises and warms the surface the air becomes more buoyant and lifts, mixing with the overlying air and dissipating the fog. Also, when the inversion “breaks” there often is an increase in wind speed, which may be slight.
This is a simplistic explanation and there are other scenarios and conditions for fog formation (advection fog, ice fog, sea fog, etc.). But generally speaking I look for fog to form when there is (or forecast to be) a narrow temperature dew point spread of about 2 degrees C or less; light winds 2 meters/sec or less; and what is the location (e.g., near a water body, swamp, in a valley, etc.). I also crudely forecast when the fog will “break” (i.e., when the foggy air at the surface mixes with the “drier” air aloft) to determine when I should plan to shoot or if I should wait for a shot – as a rule of thumb 09:00 to 10:00 am. However, as with all weather forecasts – "it depends", e.g., season, frontal passages, and the vagaries of nature. This is hardly a rigorous explanation but I hope that it helps.