So there's two parts to this. The first is that the gaseous vapor in the air does not "want to be" condensed unless it has the appropriate pressures and temperatures around it. The bottom of a typical cumulus cloud is "flat" because the stuff that's falling down beneath this surface is re-evaporating while the stuff that's above the surface is condensing. In other words, clouds are a very non-equilibrium phenomenon; they look fixed and constant but it is very similar to how a candle flame looks fixed and constant: secretly we know that the wax molecules involved in combustion are always new ones from the solid candle-body, and the candle can only be sustained if that body is being consumed. Similarly, clouds are always part of a heat-transfer process from a warmer region to a colder region.
That would not account, however, for the "puffy" tops of these clouds. To understand those, you have to understand that when the vapor condenses into a droplet it releases its heat to the surrounding air, which warms up and therefore, since hot air rises, it feels a buoyant force and heads upwards. It "pulls" the droplet a bit with it, and since the droplet is small it has a high surface-area-to-volume ratio and this "pull" is actually relatively significant. That's what causes the droplets to fly upwards and create these puffy tops of the clouds, compared to their flat bottoms.
A fog is just a cloud that is formed at surface level. The basics are not so different and just require the wind to be blowing the damp air in a direction other than upwards. If the damp air comes into a colder space, even if it blows across the surface or up a mountain, then under the right circumstances it will form those low-lying clouds that obstruct visibility that we call fog. Again, the droplets still, as they form, heat up the surrounding air a little bit and this drags them upwards a bit, so that they seem to defy gravity. Unlike in the atmosphere, there is no surface that they will re-evaporate underneath, so they eventually just fall to the ground: this is why you might get damp when you're out in the fog, as this moisture hits you on its way down.