There are a bunch of different ways you could do it. One super basic, quick-and-dirty way would be to key yourself out of the greenscreen, duplicate that layer, place it in front of your fog layers, and KF the opacity as you walk "through" the fog. So, your keyed FG layer starts as totally transparent, then becomes more visible as you move towards the camera.
if you want to get super fancy with it, you can generate some really great looking fog layers in C4D using a plugin called TurbulenceFD from Jawset. You can create fog that reacts to a solid body passing through it, then composite that into your live action footage.
Fog is merely absorption of light and color through a dense, hence it's as simple as applying a suitable color correction and animate its parameters. Of course this cann all be fancied up in a million ways as already suggested, but you must not mistake real fog for "film fog", which is actually white smoke. Unlike in movies, water-based condensation fog shows barely any visible reaction to somoen interacting with it. It's too heavy and lazy to create noticable turbulences and the particles being water, they are too transparent to really be seen.
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I would not green screen the shot unless you are very familiar with keying and compositing. You can buy a can of "fog" just about anywhere or buy some dry ice and get a bucket of water. At my local supermarket they have 5 pound block of Dry Ice for $10. Buy yourself a cheap Styrofoam cooler for a couple of bucks, cut a couple of holes in the top that are about 4 inches square, put some hot water in the cooler and have someone with an art card stand beside the cooler with a show card (poster board) and create some wind by hand. Now shoot at night, backlight and side light, put the cooler with the hot water in it between the camera and you and shoot a few takes. You'll get about 15 or 20 minutes of fog out of 5 pounds of dry ice and a little hot water. It will look much better than anything you can do in AE without spending several weeks studying the app and learning the intricacies of rotoscope, keying, simulating lighting, fractal noise, color grading, blend modes, 3D layers and a bunch of other tricks that it will take to do a convincing walking through fog simulation.
If you want to do it quick and dirty with AE, backlight yourself, throw a little side light on your face, under expose by about 1 or 2 stops, use a black background or shoot at night, then bring the footage into AE. Trim the footage to the part you will actually use using the footage panel, create a new composition from the selected take, duplicate the footage 3 times, turn off the audio on the top two copies, apply Gaussian blur to the top 2 copies with a little bit of blur on the first copy and more blur on the second copy, set the blend mode for the two copies to Screen. Now add two black solids between your footage layers, set the blend modes to Add and apply fractal noise to each layer. Solo the solid layers one at a time and adjust the parameters of fractal noise so that you get something that looks like fog slowly rolling in. Animate evolution to get the fractal noise to move. Now turn on the visibility of all layers, press the t key to reveal opacity and start at the end of the shot when you will be mostly visible. Start animating the opacity of the layers to control the diffusion on the image of you that is caused by the blurred copies of the footage with the blend mode set to Screen and the intensity and look of the fog caused by the two black solids with Fractal noise applied. You may even want to add a third black solid below the non blurred footage and change the blend mode of the footage to overlay or screen to see how that works. If you really want to get fancy, rotoscope yourself out of the shot with a loose mask to separate your image from the background, feather the edge of the mask and use that for further layering. Kind of like how you would do it in Photoshop. Plan to spend several hours monkeying around with settings and experimenting to get a decent look and figure out the AE user interface and controls.
Or, go buy a can of fog or some dry ice and have some real fun shooting the scene. If you have no budget you could even do it with an I phone under a streetlight. Just make sure you shoot in a well ventilated area. I used to shoot this wacky movie opening for Nightmare Theater using dry ice for a Seattle TV station about 40 years ago. It works just fine until one night we got a little carried away and the host almost passed out. From then on - no fog...
Here's some canned fog for you.
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