How do i fix tail lights not working

Bad bulb, bad bulb socket, bad wire... get yourself a 12v test light and find out where there isn't power and fix the problem.

you have to check the fuses to fix the instrument lights and check the switch in the top of the pedal brake for fix the tail lights.

in the rear lights you may have two bulbs one is the turn signal the other one is stop light / tail light the stop light / tail light has two filaments, one for the stop light (21 watt) & one for the tail light (5 watt) it is possible that the tail light filament is blown, try replacing the bulb to see if that fixes the problem,also check all the fuses as well.......hope this helps......cheers.

There are very few design flaws in the e46 (window regulators, sunroof guides). You just found one of them. BMW put dissimilar metals in the plug and pins in the tail light, and corrosion results. The ground connection corrodes long before the others. Cleaning it is a temporary fix. Replacing the tail light is a temporary fix. Adding a second ground connection is a permanent fix.
In the ground trace on the back of that tail light, you will find a tab for a spade fitting. Make an extra ground wire about 6" long with a spade fitting on one end and a loop on the other end that fits on one of the bolts that holds the tail light in. Do both tail lights while you are at it.
Actually, this was probably not so much a design flaw but rather a case where the plug and the tail light were made by two different suppliers who did not communicate their material selections to each other.

This is a common problem

see the final post by "yzer" for the solution:

http://www.fixya.com/cars/t870653-brake_lights_quit_working

or
Google:

Montana tail light pigtail

and you'll find numerous posts on various forums about this issue.
Sometimes its the tail lights, sometimes the brake lights or turn signal lights.

The fix involves replacing the pigtail wiring harness and perhaps, the tail light circuit boards.

brake and tail lights do not work after changing bulbs, brake switch and the fuses are good

Sounds like the fuse for the Tail Lights Is Blown.

I can't get my brake lights to work. the rear one in the window works but the tail ones won't work.do you have any ideas as of what to try to fix this problem. Thanks!
JO

Replace the tail light circuit board. They are sold at most auto parts stores.

Check and replace any blown fuses.