Painting mist or fog turns an ordinary scene into something special or specific. For example, mist can indicate that it is morning before the sun has burnt off the fog or it can indicate distance. Fog can add mystery, suspense or even peacefulness to paintings.
You should decide beforehand if you want the entire scene to contain mist of fog or just distant mountains and valleys. A scene that is fully misted will have little detail in the background because just like on a misty day – visibility is limited. Look at other paintings and at nature and observe what you see.
Let's say that the entire scene will be misted. You most likely will use opaque or rolled down colors and paint in the background, again use little detail. A dry brush technique with circular strokes makes a nice misty effect. Use slightly more detail in the middle ground and more in the foreground. When the painting is done you could use a very – very thin (watercolor consistency) white and go over the entire painting layer by layer until the effect you desire is achieved.
If the effect your looking for is mist or fog at the base of mountains or trees, then that's pretty easy too. I paint with acrylics and they dry quickly so this technique works well. After your mountains or trees are dry, dry-brush with white from the bottom upwards. Remember the mist is very transparent, so you need to use a tiny amount of paint on a dry brush. Start at the base, use circular strokes and work your way up until the mist blends in. Do the same with mountains or water scenes.
I would suggest practicing these techniques before attempting to apply them to a finished painting. If you are not comfortable, the last think you want to do is ruin your work. Remember, mist and fog are fairly simple techniques that add tons of character to art.