It's clear that Obama and Trump are as opposite as can be, in their politics, their lifestyles and their demeanour. Obama was campaigning for Hillary Clinton to be his successor and clearly feels that Trump will undo much of the accomplishments of Obama's two presidential terms. Obama will serve as president unitl 19th January 2017. He will vacate the White House around that time. He and his family plan to remain in Washington DC while their children complete their education.
It's unclear what Obama will do next.