How to make turkish coffee:
First you will need a turkish coffee pot, called a cezve or ibrik, and finely powdered turkish coffee. Espresso is not the same thing. Never try to make turkish coffee with espresso or put turkish coffee into an espresso machine. The end result will be kind of terrifying. You'll also want some small demitasse cups to serve it in. If you have a middle eastern market nearby you should be able to find everything there. Otherwise, Amazon sells all.
Mix six level teaspoons of coffee powder, six teaspoons of sugar, and a teaspoon of powdered ginger in the pot with one cup of water. Some people like to heat the water to dissolve the sugar first then add the other ingredients, but that's not really necessary. Without setting the heat too high, bring it up to a simmer. The coffee should start to foam up. Let the foam rise to the rim of the pot then pull it off the heat. This can happen pretty quickly so you will want to watch it closely so it doesn't boil over. Once the foam settles, put the pot back on the burner and let it foam again then pull it. Repeat that last step so it has foamed a total of three times. Spoon a little bit of the foam into the cups then pour the coffee before the grounds have a chance to settle out.
If the coffee is too strong or too sweet you can experiment with the quantity of coffee powder or sugar to suit your taste. Or you can play with the spicing. I like the ginger because it helps keep the strong coffee from upsetting my stomach, but some people prefer no spice. Or you could try cinnamon, cardamom, cloves, and/or a few drops of rose water. If you want to get really crazy you could try fumigating the cups with mastic smoke, or if you're really rich and you have a black market supplier you could perfume it with ambergris.
When you get to the bottom of the cup, don't drink the grounds. Tip the cup upside down onto the saucer and let it sit for a few minutes. Then you can read your fortune in the coffee grounds, kind of like reading tea leaves.