I assumed everyone just used a french press until my grandfather said he had never seen one.
Turkish coffee is made by heating a pot of water, coffee, and usually some sugar and spices until it boils and then quickly removing it from the heat source after it's begun to boil. Here's a video.
There's also 'cowboy coffee' which is just throwing the grounds into a pot of water and boiling it together, then filtering it out. This method is somewhat common with hikers (less so now because there are portable coffee makers). Here's another video.