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Fog can transform a routine scene into a moody or even mysterious photo opportunity. While exceedingly beautiful, it doesn't occur all that often, making it even more exciting to capture through your lens. Despite this, there are some outdoor photographers who avoid shooting in weather such as this. They argue that landscapes are best captured on a clear day with great visibility. Yet, to truly succeed in outdoor photography, we must learn to take any situation and work with it to the best of our ability.
Chances are, your autofocus system is no match for a dense layer of fog. Even a sophisticated DSLR will struggle to lock onto a subject successfully. The trick is to switch to manual focus and trust your eyesight to focus. If the thought of this makes you cringe, or you're an eyeglass wearer, there are new features to make this much easier than it used to be. Perhaps the best option is "focus peaking", now available on many consumer model cameras. To use it, slowly twist the manual focus ring while looking at the subject in your LCD screen. Once focus is achieved, the subject will appear to be outlined in a bright color.
Source: https://www.nyip.edu/photo-articles/archive/focusing-on-fog