The Volvo 850 hasn't been produced for over 10 years now, and that means that the remaining 850s on the road have gone through more than one set of headlight bulbs. They're not very expensive, but the halogen headlamps that the 850 uses do have one special caveat: Don't touch the bulb itself or get it contaminated with dirt. If you do, then the bulb will burn out almost instantly.
Pop the bonnet and locate the backside of the headlight. There is a plastic cover on the back of the headlamp. Peel that back using your hands.
Unplug the wiring harness to the bulb using your hands. There is a metal clip that holds the bulb in place. Pinch it to pull the clip away from the lens, and then pull the bulb out of the lens.
Place the replacement bulb in the lens housing, making sure not to touch the bulb itself with your hands or get dirt on it, otherwise you will foul out the bulb and it will burn out. Clip it in place using the metal clip, then reinstall the wiring harness and the plastic cover. Repeat the process for the other side if necessary.