I a am planning to go for a photo shoot to a place where there is lot of fog and the water droplets start getting deposited on the surface very quickly.
What are my options for protecting may camera and lens from the moisture in these conditions?
Get some silica gell, either saving packets or buying a fist-sized bag of it. Use that to help your equipment "recover" after being out in the fog, whether there are any signs or not. (Put the items or the whole kit into an air-tight container (my wife's tupperware or a ziplock bag) with the dessicant.)
For a trip to Niagra Falls, I picked up a waterproof/shockproof compact camera intended for active sporting. I kept the good stuff in the storm bag when conditions got soggy.
25 years ago I discovered an awsome fog over campus with parking lot lights looking like something out of this world. The fog was tangible. I had no second thougts firing up a Canon EOS, and nothing caused problems. Well, 20 years later the cheap "wolf" branded zoom lens seezed up; maybe it just took a while.
Then again, film cameras are just boxes.
The sensor gets hot in use: turn on live view for a few minutes, and it will be significantly warmer than the air, and will not gather condensation and will repell airborn nanodrops.
(disclaimer, I shoot with a Pentax k5, I only did a quick google about Canon and Nikon, and nothing for other brands, please feel free to add to this answer)
If you camera is not weather proof/resistant (most Pentax as are some high end Canon and Nikon), you will probably need a some sort of rain protect.
if your camera is weather resistant/proof then you should be able to use your camera safely in the fog.
Do not change the lenses in the fog, as there are a lot more chances to get water inside the camera.
Search for "Rain Protection" on most camera store web sites (most of them are quite cheap, but can get expensive).
more info (google):