Whether you plan on incubating goose eggs yourself or letting the female goose hatch them, it is important to know if the egg is fertilized. If you are incubating the eggs yourself, obviously you won't want to waste your time on infertile ones. If you let the goose sit, you don't want to let her sit for weeks on eggs that will never hatch. There are a couple of simple ways to tell if an egg is fertile.
Allow your goose to sit on her eggs for a week after she lays them. If you are incubating the eggs yourself, incubate them for a week.
Remove the eggs from the nest/incubator. Take a toilet paper or paper towel tube and shine a bright flashlight through it.
Place the eggs on top of the tube so that the light shines through. An egg that is fertile will have red blood vessels around the inside of the shell with a small dark spot in the center. This is the embryo beginning to form. Any eggs where the light shines straight through are infertile and can be thrown out.
Use an infrared machine to watch for heat spots to tell if the egg is fertile or not.