Heat about 1/2 inch of cooking oil in a skillet over med to med-high heat.
When oil is hot, gently crack egg(s) and break open right over the grease, trying not to break the yolks. If you do break the yolk and want to try again, let the damaged egg cook a bit before taking it out or you'll have a hard time of it.
Start making the toast.
Grab a spatula and wait until the bottom of the egg(s) turns white (you can no longer see the bottom of the pan through it).
Using the back side of the spatula blade (by holding the spatula normal, then twisting it in your hand 1/2 turn), splash the hot oil over the top.
Continue doing this until both the egg white and yolk have a white film over the top. This should occur just about the time the toast is ready.
Carefully remove the egg(s) to a plate and sprinkle with salt and pepper.
Serve with the toast.
To eat, break the white skin on the yolk to get to the runny goodness. Dip toast pieces in the yolk and enjoy!
Note: Until you get the hang of it, you should keep other people and pets away from the skillet while you're cooking. Otherwise, someone will likely end up on the receiving end of an over-ambitious flick of the spatula when you're trying to cook the tops. There are recipes here that describe other similar (and safer) ways to cook eggs with "runny" yolks, but if you want that old-fashioned, greasy-spoon, crispy-edged, fried-egg taste, there's just no substitute for this method.