Details are
here. Basically, you must choose "miles" in your Marriott Rewards preferences, and you start getting 4x miles with the 2d stay. Miles are point per $1 spent at the lesser brands...Courtyard,Hampton, Spring Hill, RI etc, where the more upscale full service Marriott, Renaissance, JWMs, etc, get 2 points per $ spent.
Right now, in the considerable estimation of my bud boneboybob (see his recent excellent reports on Germany), the best deals regarding FF miles are on US Airways-crappy airline to fly, but outstanding program, and Star Alliance member (think of it as getting reward travel on SQ, or TH, etc.).
Not sure how this deal works for non-US residents..check MR's T&Cs. I suspect it's probably same deal though.