It is difficult to notice fog becoming thicker, so visibility can decrease without you being aware of it. To increase your vision, use windshield wipers and the defroster to minimize any condensation on the windows. Also be sure to use low beam lights because high beam lights reflect back in your eyes. For guidance in following the road, follow the solid lines on the outer lanes.
With decreased visibility comes a decreased amount of time to react to other cars, road changes, and even pedestrians and animals in the road. At high speeds, the car can reach unseen objects in the distance before you have a chance to react to it. While it can be very reassuring to have a car in front of you to follow, you still need to keep a proper following distance. You can judge how close you are based on the skip marks--the white dashes between lanes on the highway. Each skip mark is about 40 feet apart so if you can't see any skip marks you are too close. Try to stay as far back as possible while still keeping the vehicle ahead of you in your sight. Fog also makes roads damp so braking will require a greater distance. Do not use cruise control so that you are always fully in control of the car.
Not only does fog increase the chances of having problems with keeping your vehicle on the road, but it also increases the chances of being surprised by the actions of other cars. Giving other cars the maximum amount of time to react will help to avoid accidents. Though you should not change lanes unless you really have to, when you do, turn on your blinkers well in advance of the change so other cars can react. Also, try to apply the brakes gradually so other drivers will have a chance to react and avoid a pileup.