http://www.washingtonexaminer.com/one-year-in-how-obama-gave-us-trump/article/2646127First off, Obama gave the country Trump by first giving the country the least likable Democratic nominee in modern history. Picking her as secretary of state put her in line as his successor. His refusal to pre-endorse Vice President Joe Biden in 2016 basically cleared old Uncle Joe out of the field. Also, Obama left behind a party so impoverished and indebted that party powerbrokers had no choice but to tilt the nominating process toward the corporatist fundraising behemoth that is Hillary. The fact that her campaign was sustaining the party's finances speaks to that.
Secondly, Obama helped Trump win during the campaign by lumping Trump in with all other Republicans. The intention was to make all Republicans seem icky and abnormal; the unintended consequence was to make Trump seem much more normal. In October 2016, when Clinton started posting double-digit leads in Michigan and finally pulled ahead in Ohio, Obama shifted from his tack of saying Trump “sure wasn't conservative,” to the tack of lumping Trump in with all Republicans. In Ohio in mid-October, Obama tried to lump Trump with Rob Portman, a staid and sensible establishment Republican senator. The aftermath: Portman maintained his huge leads, and Trump pulled ahead in Ohio, which he won in a blowout.
Third, and most importantly, Obama’s administration helped Trump beat Hillary, because it scared conservatives into voting for Trump. Obama, by weaponizing the federal government against religious institutions and individuals, escalated the culture war to the point that many conservatives realized no peace was possible. They were willing to vote for a man like Trump if that’s what it took to keep HHS and the DOJ from shutting down their schools and businesses. A judge on the Supreme Court who would overturn Hobby Lobby and rule against the Little Sisters of the Poor would leave freedom of conscience mortally vulnerable.
Obama’s culture warfare raised the stakes, and made Trump seem a necessary evil to many religious conservatives, probably enough to flip Michigan, Pennsylvania, and Wisconsin, and thus the election.