This is how I make it (and there are as many ways to do this as there are cooks):
dice potatoes, a bit of onion, boil in a small amount of water until tender. Add milk a heat to a slight simmer. In a mug, I crack two eggs, add flour and salt until it's gloppy-stiff. Push off a spoon into the simmering soup; simmer until done (the dumplings will float) I like a thin soup with a sturdy dumpling. I like lots of black pepper in mine.