how fogs formed?

Answer 1

When air is cooled the amount of water vapour that it can hold decreases. At the dew point temperature, air is saturated. A further fall in temperature will result in condensation of excess water vapour in the form of water droplets. If a sufficiently thick layer of air is moist, condensation can occur throughout giving rise to fog. Visibility is usually reduced to below 1,000 metres.

With no wind at all, fog will form first as shallow streaks near the ground. More usually there is a little prevailing wind serving to spread the fog evenly within one or two hundred metres of the ground. The moister the air, the greater the likelihood of fog forming under clear skies at night when radiation cooling is greatest. As with dew and frost, fog formation is most likely in low-lying grounds and hollows into which colder air sinks, and least likely on hilltops.

Fogs formed as a result of radiation cooling are termed radiation fogs. Advection fogs, in contrast, form when warm humid air from different sources passes over a much colder surface causing condensation. Sea fog in coastal areas is a form of advection fog, formed when warmer sea air comes inland passing over colder land.

Answer 2

I would only add to premi's dissertation that the water droplets forming fog are minute/colloidal and thus stay suspended by molecular collisions with air and other particles. Fog is a colloidal suspension of liquid in a gas.

[With smoke you have a colloidal solid in a gas.]