For the uninitiated, Zentangling is basically just doodling.
The Zen bit comes because when you're zentangling, you can pretty much zone out of everything else, so it's a good way to clear your head.
For more information about Zentangling, check out the Zentangle website. Zentangling can produce some really beautiful art, and a quick search on Google Images will get your jaw dropping and your fingers itching to get on with it.
For many people, they'll have been subconsciously zentangling during boring RE lessons or board meetings for years, without ever knowing that it had a name. I'm one of these.
Discovering the Zentangle website was something of a revelation - they even have Zentangle teachers!
A pretty good way to start is to just draw a loopy line across the paper, crossing over itself many times. You then fill in each space with a very simple repeating pattern. You can, however, get much more creative, and put in some very deliberate shapes and patterns, as you'll see with your Google search, and the one above, which features flower shapes.
The "proper" zentanglers only use very fine black pens, but it isn't absolutely necessary. You'll see from the example above, which was my first attempt at a Zentangle greetings card, that I've used an italic handwriting pen, and coloured pencils. It's not rocket science, just go with what you've got to hand.
Enjoy your zentangling!