Turkish coffee is thick, delicious, and if you are lucky enough to be in the right place at the right time, will contain your future in the grounds left at the bottom.
There is no secret, many Turks will happily make it for you (depending on where you are, you might actually get a fair price from a vendor) even in their homes, but there is no secret in a Rembrandt either. That doesn't mean you can do it.
There is truly nothing complex about it. A pan (cezve) is filled with water and ground coffee and heated. Percolators made this more civilized a long time ago but for the real experience not only do you need to use a simple pan, you also have to use charcoal and sand.
The sand distributes the heat around the sides of the pan and by placing the cezve deeper or more shallow the brewer controls how fast the coffee heats. In hot sand, with the cezve deep, it can boil almost immediately. You don't really want it to boil or the coffee will taste bitter, and if it tastes bitter you are doing it wrong. You'd rather have a more medium heat so it just starts to form bubbles after 8 minutes or so.
Today they don't use charcoal, they use propane. But for tourists they still use sand so you can enjoy watching that process.