There are almost as many ways to teach Go as to play it.
Whatever way you do it, it must be simple and easy to understand. Do not include too much in the first lesson. Certainly teach how to place stones (and that they do not move), how to capture stones and what the aim of the game is (control more than half the board). You may also like to explain the concept of territory.
The main thing is to get them playing quickly against you and talk them through extra concepts, for instance eyes and ko, when they occur.
Best is to play handicap games, for instance 5 stones (or even 6) on a 9x9 board. However always describe this as a head start, not a handicap, as people think handicaps count against them. However watch out for the ringer: the old guy who says that he played once or twice at the London Go Centre in the 1970s, who after you have given him 5 stone start reveals he was 5 kyu.
Always encourage the student. Never criticise them for misplaying a joseki for instance. If they play into atari say that it is a trap, but sometimes it is good, though usually is not.
After their lesson give them the leaflet with the rules and more in for them to study. Often they do and come back the next day with questions and the desire to play more.
Do not try and run a tournament for the beginners, unless there is a captive audience who have been around for several days and contantly returning to play. Most people just want to play once and move on, with the option of a pressure free second game if they return. Also it would take up a lot of space and resource which would be better used for teaching.
Always have a stock set of answers mentally prepared for the usual questions that students may ask, though there is usually one question that you have never thought of before.