The trick to cooking eggs is butter -lots and lots of butter.
Bacon grease works, but it puts big bubbles in your eggs when you do them over-easy.
If you are making omelets, again, use lots of butter. Make sure you let the butter cover your entire pan, even up the sides as high as possible. If you use enough butter, you wont even need a spatula to make an omelet.
Scrambled eggs are always going to stick a bit in my experience, because you push the butter away from and off of the pan when scrambling. This means a little cleaning duty, and I dont like cleaning -so I stick to eggs over easy and omelets. Of course hard boiled is great too.
I love eggs.
-the bravest man in the world was the first man to eat an egg.