Evan Osnos has a very good article in The New Yorker (subscription required) on the mechanics of getting a president out of office.
Basically there are two ways to get rid of a president: impeachment or through the Twenty-Fifth Amendment, Section 4, which allows for the Cabinet or other designees appointed by Congress to certify the president is incapable of fulfilling his duties.
How likely is it that either scenario will take place? The Twenty-Fifth Amendment, Section 4 requires that the majority of the Cabinet — people appointed by the president — sign off on his disability. That’s not going to happen without some medical emergency or state of unconsciousness; they all think that when he farts they’re hearing Tony Bennett croon. This Congress will not pass any law that takes over that duty. So unless Trump is struck by lightning, he’s safe.
Impeachment is another route, but history has shown that only happens when the opposition party is in control of Congress where the articles of impeachment are drafted and voted on. With all due respect to Rep. Maxine Waters (D-CA), that’s not going to happen until the Democrats take over Congress again. So the earliest that could possibly happen is in 2019 after the Democrats sweep the mid-terms. (And how likely is that?)
The only other way out is through resignation when the president realizes that he no longer has the support of the people and Congress. Given Trump’s propensity for delusion, that’s not even on the horizon; he’d think he’s doing great even as they handcuff him.
As Osnos notes, it requires a certain level of delusion to be president in the first place.
The history of besieged Presidencies is, in the end, a history of hubris—of blindness to one’s faults, of deafness to the warnings, of seclusion from uncomfortable realities. The secret of power is not that it corrupts; that is well known. “What is never said,” Robert Caro writes, in “Master of the Senate,” about Lyndon Johnson, “is that power reveals.” Trump, after a lifetime in a family business, with no public obligations and no board of directors to please, has found himself abruptly exposed to evaluation, and his reactions have been volcanic. Setting a more successful course for the Presidency will depend, in part, on whether he fully accepts that critics who identify his shortcomings are capable of curtailing his power. When James P. Pfiffner, a political scientist at George Mason University, compared the White House crises that confronted Nixon, Reagan, and Clinton, he identified a perilous strain of confidence. In each case, Pfiffner found, the President could not “admit to himself that he had done anything wrong.” Nixon convinced himself that his enemies were doing the same things he was; Reagan dismissed the trading of arms for hostages as the cost of establishing relations with Iran; Clinton insisted that he was technically telling the truth. In Pfiffner’s view, “Each of these sets of rationalizations allowed the Presidents to choose the path that would end up damaging them more than an initial admission would have.”
Law and history make clear that Trump’s most urgent risk is not getting ousted; it is getting hobbled by unpopularity and distrust. He is only the fifth U.S. President who failed to win the popular vote. Except George W. Bush, none of the others managed to win a second term. Less dramatic than the possibility of impeachment or removal via the Twenty-fifth Amendment is the distinct possibility that Trump will simply limp through a single term, incapacitated by opposition.
The most likely scenario for him leaving office before his term is up is that he will decide being president is for losers and he’d rather be playing golf. The problem with that is the country can’t wait for him to figure that out.