Pop the hood and get to the backside of the lamp in question. There will be an electrical dongle screwed into the back of the lamp unit. Disconnect, and carefully pull the old bulb out. Simply pop out the burned bulb, plug in a new one. When re-seating the bulb, make sure to tighten the screw assembly otherwise water could leak in and short your new bulb.
The headlight unit must be removed to replace the bulbs, not enough room to get your hand in behind the bulb sockets.
1. Make sure headlamp is off and open hood.
2. Taurus model years 1990-1999: you must remove the whole headlamp to replace the bulb. Not a horrible task. Just annoying.
3. Facing the driver's side headlamp, and looking at the headlamp itself, at clock positions 8, 11 and 1 are the headlight housing screws. They all look the same. Using a 10mm socket wrench, remove these 3 screws and set them aside.
4. Just to the right of the "11 o'clock" housing screw is a bolt (same hexagonal 10mm sized top as the housing screws). This just needs a few turns to loosen it.
5. Gently pull the whole headlight forward. Now you can get at the bulb.
6. Disconnect the electrical connector from the bulb. Now the headlamp is free to work with. Remove the bulb, replace with a new bulb, make sure the bulb housing cylinder is in place and reconnect the electrical.
7. Place headlamp back into position. Line up screw holes. Tighten the bolt. Replace housing screws and tighten.
8. Passenger side headlamp is mirror image of driver's side. Screws at 11, 1 and 4 o'clock positions. Bolt should be to the left of the "1 o'clock" housing screw
This was helpful info, but not correct for my 1992 Taurus. There were no 10mm screws and the bolt only secured the side running lights. The three attachment points contain long adjustment screws, much smaller then 5mm. At the end of each screw, closest to the radiator, are rubber plugs held in place with metal clips. Remove the metal clips and the headlight assembly pulls almost straight out. These attachment points are all plastic and easily broken by those not knowing how to remove the headlight unit.