Always start with a hot skillet.  Melt the butter with oil on medium-high heat being very careful not to burn the butter.  To test when skillet is hot enough to add the eggs,  add a drop of water to the skillet.  If the water sizzles then then you are ready for the eggs!

Start with one egg and crack it gently into a small bowl.

Carefully slide the eggs into the skillet one at a time.

Cook the eggs for about one minute until the outer edges of the egg start to turn white.  Lightly salt & pepper your eggs as they cook. Add a couple teaspoons of water and lower the heat; cover the skillet with a lid. Let eggs cook for about 3 more minutes.