Halogen bulbs work by placing a tungsten filament inside a tube containing a halogen element such as iodine. When electricity passes through the tungsten filament, it heats up and emits light. Like normal light bulbs, the filament is slowly expended, but unlike normal light bulbs, the halogen reacts with the tungsten gas and redeposits as tungsten on the filament. This process enables halogen bulbs to last much longer than normal bulbs. Even so, they will eventually need to be replaced.
Purchase a replacement halogen bulb. Because of the wide variety of halogen bulb sockets, you need to make sure that the replacement bulb is the same model as the original. There should be a three letter code somewhere on the bulb that you can use to find a replacement. If you cannot find a code, try searching for a new bulb with the same volts and watts that has the same look to it.
Turn off the old bulb, if it is still working, and give it a few minutes to cool down. Halogen bulbs get extremely hot and need some time to cool down before you can touch them.
Put on cloth gloves before you handle a halogen bulb. Oils from your hand can cause the bulb to heat unevenly and shatter. If you do not have cloth gloves, you can use a napkin.
Remove the old bulb from its socket. This procedure will be different for each different type of socket. Some will have you push down and twist to unlock the bulb, others may just have you pull on the bulb to free it, and still others may screw into and out of the socket. You should be able to determine the correct method of removing the bulb by examining the socket.
Insert the replacement bulb into the socket. It is extremely important that you use gloves or a cloth while handling the bulb. Do not get the glass dirty or oily.
Turn on the power to the lamp to ensure that the bulb lights up.