Having enjoyed a wonderful Turkish coffee in a Turkish restaurant in London I decided to make some myself. I bought the fine ground coffee and a cezve I made what turned out to be an unappetising mud! What's the secret of making Turkish Coffee?
Pour it in your cup(s) while it's hot and let it rest after making. No milk or sugar added, because it means stirring and the leftover grounds won't deposit to the bottom of the cup. Or add the sugar along with the coffee before brewing.
As for brewing, it's customary to bring it close to boiling until it foams (slow heating, and stirring the pot a little), pour some foam into cups, then boil it again. In any case, turkish coffee is always brought to a boil twice.
Traditionally it's made on hot sand, which assures slow heating, and stirring the cezve by just holding the handle is easier, by doing it in broader motions.
You could also let grounds settle in the cezve and just be careful when pouring. Then you can add milk if you want. But that's not the turkish way, it's the east european way.