The truth is that "Zen" has become a commonplace word and placeholder in our culture for anything deemed "mystical" or even trendy. Along the way, its original meaning -- not to mention its power -- has been somewhat diluted.
Unlike most other forms of Buddhism, Zen is premised on the notion that all beings are already Buddhas and merely need to tap into that awakened consciousness. The various techniques of Zen are thus aimed on breaking down the preconceptions and mental blockades that prevent individuals from realizing their awakened nature.
As the literal meaning of its name ("concentration") suggests, the central technique of Zen is meditation. Through focusing on the most mundane of processes, such as breathing or walking, meditation forces one to be entirely in the moment, divorced from all exterior distractions. While it sounds easy, it's actually incredibly difficult, though over the years medical researchers and neuro-scientists have become interested in the biological processes and benefits of meditation. Can it diminish stress and anxiety? Lower pain response? Increase immune system function? It will be interesting to see where the literature eventually ends up on those and other questions. From the standpoint of Zen practice, the intense focus of meditation is meant to cut through all of the obstacles to discovering one's Buddhahood resting beneath the layers of overthinking and preconception.
A second technique, used to varying degrees throughout the subsets of Zen schools, is the riddle or "koan." Certainly you have heard of the most popularized ones, such as, "What is the sound of one hand clapping?" Of course, many years ago Bart Simpson claimed to solve that one:
"When you can do nothing, what can you do?"
Or, "When you have a staff, I will give it to you. When you have no staff, I will take it from you."
If your first reaction is to furrow your brow and curse, you're on the right track. All due respect to Bart, the koan does not ask for a clever or intellectual response. It's meant to break down the part of your rational mind that overthinks, and thus keeps you from realizing your inherently awakened state. Zen masters give these to students to drive them to the edge of insanity because it's at that edge -- between reason and madness -- that awakening is found. Huston Smith, one of the elder statesmen of the discipline of Religious Studies, recounts that very experience in a Zen monastery. This hasn't stopped people from having fun with the concept of koans, as in this video, which I first learned about from a former student: