First things first: gather the necessary tools. A screwdriver and a cloth.
Luckily, you'll mostly only need a manual screwdriver to remove the panel. You will also want to have a soft, non-abrasive cloth handy to help avoid any contact with your fingers and the lamp assembly. A Micro-Fiber cloth is highly recommended, and widely available from most supermarkets.
Turn off TV or Projector. After the unit has cooled down properly, remove the power cord from the outlet and the unit completely.
Remove the bulp compartment door. The lamp compartment on projectors is usually located underneath the projector unit. Remove the screws and the lamp compartment door should lift off nicely.
Remove the lamp assembly. Be carefull and pull out the lamp assembly. Disconnect any power cords that may still be connected to the lamp assembly. Put the bulb to one side for recycling.
Clean the lamp compartment. Dust gets everywhere and while you have the projector open, use a soft cloth or micro-fiber cleaning cloth to remove any loose dust from the lamp compartment.
Insert the new lamp. Carefully re-connect power cables to the new lamp and slide the new lamp into the compartment in the same way that the original lamp came out.
Replace lamp compartment door. Set the lamp compartment door back into place and securely screw in the door without screwing it in too tightly.
Reset the lamp timer. Instructions on how to do this should be covered by the instruction manual. You're Done! Enjoy your projector again and make sure you have a backup lamp handy in case the lights go out unexpectedly.