This is the only way to make Turkish coffee. The style is different from espresso, and in my opinion superior when made properly.

Requires patience and watching. The coffee grind must be right, and some practice is necessary.

Cezve is the correct Turkish term for what is commonly called an Ibrik in the United states. Ibrik is the Arabic term, and thus not used by the Turks themselves.

Coffee making in the Cezve provides a simple solution to the problem of fresh grinds and roasts. The procedure is as follows.

Add the ground coffee to the Cezve, and place the pot on the stove. Gently roast the grind, turning over with a spoon to ensure uniform roasting. When the roast is almost done, add the sugar if you like your coffee sweet. Mix it up well with the grind, and finish roasting. Add water, when the water boils raise the Cezve so that it settles down, and then bring to boil again. Pour out in cups. Let the coffee rest for a few minutes, so that the coffee particles settle down. If you give it the five minutes then the coffee shan't feel gritty as numerous reviewers have complained. Leave the last few drops with the sludge in the cup.

I should add that we have been making coffee like this for a while and have never had any trouble with grittiness. A little patience is all that is needed.

To get the best results from a Cezve, it is important to get the grinding and the roasting right.
The grind should be as fine as possible. Now for the roast. If you want to roast your own, then go for a light roast. The final roasting is done in the Cezve, so if your roast is already too dark you are not going to get the right effect. Remember, the lighter the roast, the more acidic the coffee and the higher the caffeine content. So you should experment a bit to determine what you like best. There is a Turkish brand called Turkmeck available in many middle eastern stores that is more or less right for this.

The trouble with making coffee at home is that one does not roast and grind coffee everyday, so there is the problem of coffee deterioration. I store our coffee in VacuVin jars, they give satisfactory protection. The Turkish approach is to grind the coffee, but keep the roast light so that the deterioration is minimal. Then the final roasting is done in the Cezve. Since the amount of coffee is small, it is not difficult to get a nice uniform, dark roast quickly. If the roast is dark already, then the results are not likely to be good.  

Of course the water should be as good as one can get. So use filtered water.

The Cezve we use was brought by my roommate from Turkey. It is an authenic brass handmade Cezve, so don't expect the sleek lines of  modeern Cezve. It is small and narrow, just right for about two cups of Turkish coffee, and in my opinion gives better results than the more modern ones.