Summarize:

Pour the oil into a large nonstick skillet. Set the pan over medium heat for approximately 1 minute. Let the oil get hot, but do not allow it to start smoking. When the oil starts to glisten, turn and rotate the pan to help spread the oil across the entire bottom. Carefully crack each of the quail eggs into separate ramekins.  Since quail eggs are so small, they can be difficult to crack without breaking the yolk. The easiest way to break open the egg is to saw off the end using a serrated knife; dump the contents of the shell into the ramekin afterward. Alternatively, you can carefully peel off the end of the shell with your fingers and pinch the inner membrane to break the egg open. Pour out the contents from that hole.  If you decide to cook more eggs than called for in this recipe, work in small batches, preparing about four eggs in each one. Pour each quail egg out of its ramekin, allowing it to gently slide into the hot oil in the pan.  Place the edge of the ramekin as close to the pan as possible to minimize the drop distance and preserve the yolk. Try to position the eggs so that they do not touch inside the pan. Cover the pan and cook the eggs for 1 to 1-1/2 minutes, or until the egg whites are firmly set.  Do not touch the eggs while they cook. Note that the yolk will not appear firmly set when the eggs are finished. Use a spatula to carefully lift each egg out of the skillet and onto separate serving plates. Season with salt and white pepper, and enjoy them while they're still warm. Fried quail eggs can be served as a standalone dish, but they're more commonly served over other dishes, like slices of baguette, smoked salmon, or crab cakes.
Heat the oil. Crack the eggs. Slide the eggs into the oil. Cook until firm. Serve warm.