I use an old southern method called Frog in the Hole (also known as Eggs in a Basket). It's close to sunnyside down, so I voted that way. My personal variation combines the best attributes of a fried egg and a grilled cheese sandwhich.
Get one egg, one slice of favorite cheese, spreadable butter or olive oil, and two slices of bread. I put a pinch of allspice in my eggs, but you add your favorite omelet bits.
Spread butter or olive oil on one side of each slice. Use a cup or glass to cut out a circle in one slice. Remove the circle and set it inside a skillet. Put the cut slice in the pan also. Crack one egg and drop it inside the hole in the break. If the yolk breaks, that is okay.
Cook the egg inside the bread. Your little circle of toast is your guide. Check it to make sure your toast isn't burning. While the egg is cooking, brush some more butter or oil on the side facing up. Also cover one side of your second piece of bread.
It's time to flip the egg. You want your egg cooked enough that it has solidified for flipping. Flip both the bread with the egg and the little circle. While your egg finishes cooking, place your cheese slice on top of it. Top that with your second slice of bread, butter or oil side facing up.
Your circle is still your test sample. When it gets crispy on the pan-facing side, you are going to flip again. Flip the entire sandwhich so that the ungrilled butter or oil is now facing the pan. This last stage is melting your cheese. After about a minute, use a spatula to plate the circle of toast and the sandwhich egg-side up. Serve warm with a fork.