Over easy and sunny side up are two of the common ways your guests will ask for their eggs. Each one is a variation of a fried egg and each one requires the yolk to remain in liquid form and intact during the process. A delicate touch is needed for either type of egg to work, but if you're able to stick to the crucial points of each preparation, you'll deliver an ideal over easy or sunny side up egg every time.
Over Easy Tips
Eggs "over easy" means that they are fried on both sides with one flip, but the yolk still stays runny. Use medium heat so the egg won't cook too quickly, and use a non-stick pan if possible or use about a tablespoon of vegetable oil or melted butter to prevent sticking. Every egg has a noticeable inner white and an outer white. The outer white will set and cook first, so watch the inner white as the egg cooks, and once that inner white appears set, flip the egg gently. You can try to flip it gently with just the pan, or use a spatula if you're not confident. Allow it to cook on the other side for less than 20 seconds, until all the white is set, then slide it onto the plate.
Sunny Side Up Tips
A "sunny side up" egg is a fried egg that isn't flipped at all. You cook it on the bottom, but the top part of the white is just barely set and the yolk sits up there like the sun. To get the yolks and the top and bottom whites cooked right, crack them into the skillet over medium heat initially, then move them into a 350 degree Fahrenheit oven. Use a non-stick pan that is oven safe, or add a tablespoon of vegetable oil or butter so it slides out easily when finished. It should only take about four minutes in the oven to set the top of the eggs without burning the bottoms. Try a cover on the skillet over low heat if an oven isn't available.
You may prefer just cracking your eggs directly into the pan to start frying, but to maintain the highest quality, consider a different approach. Whether it is sunny side up or over easy, many cooks like to crack their eggs into a small dish before adding them to the pan, just in case all is not well inside the shell. It's not unheard of for eggs to have visible membranes or blood clots inside, and it's easier to discard a bad one if it hasn't been in the pan with other eggs first.
On the Safe Side
Some government recommendations on how "well" to cook eggs tend to conflict with the yolks of a sunny side up or over easy egg. The Foodsafety.gov website recommends cooking eggs until the whites and yolks are firm and 160 degrees Fahrenheit. Food borne bacteria can be part of raw eggs, so ensure your whites are always set and cooked and the yolks are heated through, if not cooked firm. Also, buy your eggs from vendors with a solid reputation for selling high quality eggs, to minimize any risk.