How to Fix Foggy Tail Lights in BMW 528 car?

they make special paint for this, contact a local automotive paint store they can sell u the paint and the cleaners you need to use to prep the plastic, do no skip any step, what follows is a detailed description of what this cleaning entails.
Use a clean rag and the soapy water to wash the rest of the dashboard. You'll need to scrub especially hard if the dashboard has Armor All™ or another type of protectant on it.

Next, rinse the dashboard off well, and dry it off with a clean rag. Before you paint the interior of your car, the areas will need to be completely dry in order for the paint to stick well to it. So, let the dashboard air dry while you apply painter's masking tape to the interior. Painter's masking tape is blue tape that peels off easily after the job is done. That's why it's recommended over regular masking tape. Painter's masking tape won't leave a sticky residue like regular tape can, too.

Tape off the areas of the dashboard you don't want to get paint on. This may include the bottom part of the windshield, the radio, gauges, the gear shift, other chrome, etc.

Before you paint hard plastic areas, you'll need to rough it up with a piece of fine sandpaper first. Use an old rag to wipe up the dust the sandpaper creates. Then, you'll need to remove the remainder of the dust with a wet, soapy rag. Rinse the area again and dry it well.

Finally, use a clean rag and some rubbing alcohol to go over the plastic pieces, and the dashboard (if it's made of plastic) one more time. The rubbing alcohol will remove any residue left from cleaning the area with the soapy water.

You'll need the following. Painter's tape or Masking tape, 2000, 2500, 3000 grit sandpaper, bucket of water, headlight polish (PlastX, etc) and microfiber cloths

Mask off around the light so you don't have to worry about sanding your paint if your hand slips.

Soak the sand papers for at least 15 minutes. The more water the better Using the lowest grit, start sanding in ONE DIRECTION ONLY,(side to side). Keep the sandpaper wet and dip it in your bucket of water frequently. Now dry the headlight and it should look all hazy

Switch to the next finer grit, and repeat the step above, but this time go in the OPPOSITE DIRECTION (up and down). Keep using water
Dry it again, and it will look better than the first time.

Repeat the process again with your finest grit. Again, OPPOSITE DIRECTION with plenty of water. Dry it off. It should look relatively new at this point. Remove the tape as it will contain bits of grit from the sandpaper.

Generously apply the headlight polish in a circular motion to the headlight

Using your microfiber cloth, rub off .. repeat several times with FRESH rags until the polish is dry and gone.

Now the headlight will look like new

sand it down with some fin grit sand paper, apply a slight coat of rustolium, masking off the area with masking tape, so you dont create a larger area. Then ge touch up paint from your local dealer, some thinner and a refilable pray can, thin the touch up paint with the thinner in a 2 part paint to one part thinner ratio and spay a few coats on, should work.