Depending on where you are from, where you have it and who is making it you might call it Turkish, Greek or even Macedonian coffee. This is how I learned to make it from a Serbian guy named Mille Vukelich. ...well sort of. He just called it coffee or good coffee, sometimes "real" coffee and the method was as important to him as the resulting coffee.
No matter what you call it, this is the strongest variant of coffee I have ever encountered. It's fantastic stuff that is best consumed in moderation. It's somewhat like what Americans call cowboy coffee. In the Mediterranean regions that are known for it there is a lot of social ritual that surrounds both making and drinking it in this style. Some of those rules are important and others not so much. It's that whole anthropology of culture making the necessary seem obligatory thing. So, don't feel bound to the rules but at least know the ones you are breaking.
There are other Instructables that show how to make traditional "Turkish Coffee". This one is pretty good. www.instructables.com/id/How-to-Brew-Turkish-Coffee/ My Instructable is a little more on the "whatever let's just make the stuff" side.
So, with all due reverence to tradition before we chuck it out the window, lets make some potent coffee!
Step 1: What You Will Need
You don't need much really. Just get some "Turkish ground" coffee in the darkest roast you can find. You can easily grind it yourself either at home or where you buy it. I'll explain that in the next step.
Something to make it in. The traditional tool is a most often called an ibrik. You can find these in any number of specialty shops and on line. The "ibrik" in the photo is not actually an ibrik. It's a "milk warmer" that is shaped almost exactly like an ibrik. I have also used large stainless steel measuring cups, Pyrex lab glass and on a couple occasions, stainless steel water bottles. The point is the traditional tool is good but not essential. Don't let not having one stop you from making "Turkish" coffee.
Sugar, any sugar will do but I like sugar in the raw or brown sugar. According to at least one Serbian, I like waaay too much sugar. I'm going to get diabetes how can I even taste the coffee amounts of sugar. Sugar to taste is the key phrase here. If you are new to coffee or even just Turkish coffee you will probably have a more enjoyable experience drinking it sweet. This will be stronger than espresso so guess based on how you might approach that.
Water. Yeah, whatever is available.
Heat source. I have made Turkish coffee over campfires and stoves, on hot plates and Bunsen burners. The only important thing is that you be ready to either turn the heat down quickly or remove the cooking vessel from the heat quickly. This simple but important maneuver during the "boiling" can make a big mess if you don't anticipate the need to immediately reduce the heat.
Demitasse cups are best but not critical other than making you feel exotic and making it harder to absentmindedly swill way too much of the stuff.
Step 2: The Coffee
You want the darkest roast possible. Most French roast is good.
Mille insisted on using an old hand grinder and we took turns grinding the coffee. It was an important part of having coffee together. I believe it did enhance the experience and it gave time to pause and chat a little.
You can use whatever method you like. Grocery store grinders usually have a Turkish grind setting on them but you might want to dump your ground coffee through a second time. You'll want it ground very fine but not quite powder. If it's not ground fine enough it'll float. That's no good. You aren't going to filter it.
Step 3: Getting Started
First put some water in your cooking vessel. I didn't measure anything. It was about two cups. You probably want to use enough water to fill whatever you are making coffee in to about the half way mark. This will become more clear in the boiling step. You actually need it to froth up to the top so too little water and it won't get there. Too much and it doesn't have room to boil and get frothy.
I also just add coffee until it "looks right". Using a mildly heaping tablespoon of coffee for each cup of water is a good place to start and then you can add more or less to suit your taste once you've made it a couple times. This is the only thing Mille says I do right most every time.
Adding the sugar is both optional and done to taste. When I order it sweet in restaurants I get about the same thing as when I make it. Some people drink it black.
I have never seen anyone add cream to this type of coffee but cinnamon, nutmeg and cardamom are fairly common.
Step 4: Boil It
You will need to boil the coffee "several times". That's just a cycle of heating it to a frothing boil and then taking it off the heat a few times. This mixes the coffee very well and there is a noticeable difference between the way it looks after each cycle.
You will need to go through the process of boiling and pulling it back about three times. That's the one traditional thing I stick to. Two boils isn't enough to properly mix and isn't enough time to get the flavor out of the grounds. Four or more can sometimes make the coffee taste a little flat. That is only my opinion so experiment and see what you like. I have also been told it's bad luck to froth it more than three times. I figure that's as good a reason as any to follow the "recipe".
Step 5: Pouring the Coffee
This is an important step. The "pot" will have quite a bit of silty grounds in the bottom. It's unpleasant to get a mouthful of them. If you are pouring several cups and especially if you are sharing, you should be, you need to be careful about the sludge.
Do not agitate, mix or stir.
Just pour the coffee.
This type of coffee is traditionally enjoyed in groups. It's a chance to slow down, have a conversation and take stock of your day. While it's perfectly acceptable to drink coffee on your own it's as good a reason as any to spend a few minutes with a friend. That was certainly the most important part to Mille.
Drink your coffee slowly. It took some effort to make it and while you could "get it to go" it's not well suited to that. You'll likely mix up the grounds as you walk and probably drink it down to the last and get a mouth full of sludge.
This is also a great way to have coffee while camping, hiking, rafting, etc. and a stainless steel water bottle makes a great coffee pot for Turkish style brewing. You don't even need an extra piece of equipment.
Once you get used to it you can also pre-mix your coffee and sugar so you just need to add water and heat it!