From ESPN

This particular ERA (Equality in Row Assignment) appears to be a nation-by-nation battle. USOC communications chief Patrick Sandusky said U.S. teams, regardless of sport or gender, are given one economy-class ticket per athlete, coach and official. (U.S. teams fly on official sponsor United Airlines.) Individuals can choose to upgrade on their own dime if they wish, he said.

They said this because in response to the stories about some countries putting the men in business class and the women in Economy

I believe the USOC pays for the seats, they usually fly scheduled flights (there are tons of stories about this team or that team being on a plane full of people)

From a wrestling publication

I flew with the Greco team from Colorado Springs to Chicago today, and as you might expect, there is a buzz and excitement among the guys. Justin “Harry” Lester, despite being seated in the back of the bus for the flight to Chicago, is as eager to compete as I have ever seen him. He has won two World bronze medals, but he is ready and focused to deliver on the World’s biggest stage in the Olympics.

A huge cheer went up on our United Airlines flight to Chicago when it was announced that the U.S. Olympic wrestling team was on board. The U.S. women and freestyle teams will be heading to London in the next couple of days.