Someone (you know who you are) asked me to post an example of a Zentangle I've made, and here's a shot of the latest one in my home journal:
One this size takes me about a month to finish; a normal person could probably draw it in a couple of hours. I don't do too many because I prefer working in color, but I do make them mainly when I'm on the phone either with doctors or NY (which is also probably why mine are so convoluted/complicated.)
To draw them I just use a fine black Sharpie pen (see below), the kind that doesn't bleed through paper. I know the Micron pens are supposed to be better for detailing, but the barrels are slippery and I don't have enough motor control to draw with really fine detail anyway, so they're wasted on me. I also draw them in a lined journal because the lines help me keep my doodles relatively uniform (plus they're great for when I want to fill in a spot with bricks.)
Making Zentangles is very relaxing and mind-clearing for reasons that are utterly beyond my comprehension. I've never bought the kit from the official web site, but I suppose I should someday so I can learn all the little tricks and techniques.