A greek coffee is served in a small cup, think espresso size. There will be 2 inches of coffee, and at the bottom, one inch of grounds. If there's someone with a little imagination then it's fun to read the trail the coffee grounds leave.
Ideally you swirl the grounds around and turn the cup upside down on the saucer, turning it 3 times if I remember rightly.
K and I had our morning coffee at the cafe and while the men were discussing fishing or soccor or something equally entrancing I took a photo of his cup. No turning it upside down and swirling it around.