I like wiping the inside of each cup with a small dab of butter. Even using non-stick it helps with releasing the cooked egg. Heat 1/2-3/4 inch of water in the pan brought to a hard boil.
Put in the eggs and cover for 3-1/2 to 4 minutes for soft boiled (cooked white, runny yolk). I carefully use a silicone spatula to remove them while holding the egg cup pan directly over the serving plate. (The reason for the slot is for inserting a fork to remove and hold the hot egg cup pan.)
I like mine on toast, or for making eggs Benedict.
"Food is our common ground, a universal experience." - James Beard