Turn the power switch to the off position in the fuse box of the house. Stick a paper note on the fuse box letting people know that electrical maintenance is being performed.
Set up an A-frame ladder beneath the light fixture and climb up to the light. If the light cover fastens above the light bulb, remove the light bulb from the socket by turning it counterclockwise. Undo the screws that hold the cover to the light fixture. If a sort of glass globe covers the light bulb, look up above the globe to locate the fasteners holding it to the fixture. Some screws may need to be removed with a Phillips or flathead screwdriver depending on design. If the light cover fastens beneath the light bulb, go to the next step.
Locate the fasteners and remove them. Some covers have a nut that has to come off the threaded fixture bolt that protrudes through the center of the light cover. Turn this counterclockwise while holding the cover. Once it comes off, slide the cover down and off the end of the threaded bolt. If you can't find any fasteners, try twisting the cover to the left. If it loosens, it means that the cover itself is threaded onto the fixture. Keep twisting to the left until it comes free. If it doesn't loosen, there may be a decorative plate that hides the screws. You need to locate and pry this plate off before you can access the fasters holding the cover to the fixture.
Take the cover to your local home improvement or home lighting store and show it to an employee. Ask if they have the same or something similar to the cover you have. If you don't want the same cover, ask them to point you to covers that may not look the same, but will attach the same way as this one does. Install the new light cover in the reverse order that you removed it.