My preferred way of making them is:

• toast the bread in the toaster first (it could be toasted in the pan with butter, though that's less healthy)
• use something round to cut one or two holes in the bread (two holes provides more structural integrity, since it effectively allows for a cross-brace... it's also more flexible, allowing many more shapes of bread to be used):
  • one ~2.5" hole, using an upside-down glass
  • two ~1.5" holes, using a bartender jigger
• preheat pan so that egg white will begin to solidify as soon as it hits the pan (ie. won't totally run under the toast and all over the pan)
• drop the egg in each hole, keeping the yolk whole (if using two holes, separate the yolk from the whites, and pour them in separate holes)
• (optionally) pour lots of pepper or Dave's Insanity Sauce on top of the eggs
• once the bottom of the egg whites solify enough to retain structural integrity (judge by how much has turned white/solid), turn each slice over, without breaking the whole thing apart
• ASAP, while the top is still hot, put some shredded cheese on top, put the lid on, and cook until the cheese is melted (based on how long you cook it on each side, you can lean towards being more runny (and more likely to fly apart), or more solid (and less likely to fly apart))

Optionally serve with:

• Ham that's been heated in the same pan
• Mayo + mustard mixed together