With the Deepwater Horizon incident in the Gulf of Mexico, there never was that much interest from the public on how a well is being drilled in over 5,000 feet of water. The video below is a presentation given by some colleagues from Shell at the Aspen Ideas Festival. The presentation describes the different processes that take place during drilling and the barriers that are inherent part of any well.
Make sure to listen to the Q&A session after the end of the presentation. It provides additional insight on this terrible incident.