i was just out this morning and it was easier than i expected. i found that overexposing created the illusion of denser fog and underexposing the reverse.
I'll know better when i get home and look at them on the full screen.
There are 2 steps I use to lessen the hazy blurryness.
Break out the channels into RGB and see which one is clearest, often most of the blur is in the blue channel. Desaturate the individual channels and mix the opacity to get the amount of punch you want. Now you have a nice B&W image and you can set that to luminosity to govern the gamma of the image.
the other step, sometimes used with a luminosity channel, sometimes on its own for lighter fog, us to use a wide USM (around 80 pixels wide , 30-40%) and a slight tightening of the S curve.
That is assuming you want a light fog to go away. If you want to punch up an existing slight fog, just do the same steps backward.
There is no 'correct' way to shoot fog. However, unless it is dark out, I would recommend to overexpose by a stop or two. Your meter will want to make the fog look middle gray, when it tends to work better closer to whitish.
Non technical advice would be to move and shoot as quickly as possible. Depending on the weather is can look great when you look out the window and be gone once you start to setup the shot. Suprises and exploration is fun but having a location in mind before you go out if you know it'll look great with fog is something I've been working on. I need to set my alarm one hour earlier uggh. It goes fast around here. Of the two fog shots I've taken and really liked, one was a lucky accident.