Long story short: it's gonna play out a lot like Rob Ford, but shorter.
Long story long:
Trump gets inaugurated. Initially most of the Republican caucus plays along with some of his less-asinine policy planks, but I doubt any wall gets built. He pisses off an ally or two -- maybe he'll have a beer with the president of Taiwan, perhaps? -- but after a while most world leaders just try to avoid and ignore him.
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Trump: "Hey, president of West Slobovia, you really should come on over to America. It'll be tremendous."
President: "Uh... thanks, Don, but I've... got a thing. It's over in East Slobovia. Gonna take a while. Whoops! Toaster's on fire, I'll call you back." (click) *
Trump, on Twitter: "West Slobovia's leader is weak. Can't even take flaming kitchen appliance. As overrated as M. Streep's career. SAD!"
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After about eight months, some prominent congressional Republicans start to cautiously speak out openly against Trump. He fires back with something ridiculous and offensive, because he's a ridiculous person with the thinnest skin imaginable. But, this just gets the ball rolling.
Behind the scenes, and tired of his antics, some bigwig Republicans will work with the inteligence agencies Trump seems to love to antagonize to cook up something bad enough to get him impeached, and eventually forced to resign (or perhaps removed forcibly, after having done something clearly unconstitutional). Trump will lawyer-up, but it'll be futile and he'll be removed from power. My guess is that he'll be president for less than two years.
Now, it doesn't matter if the thing that brings him down is real or not. It looks like there's probably enough awful stuff floating around out there that you don't really need to make something up; you just have to package-up some bad things he's done in the right way, sell it to the American public, and there you go. I mean, hell, a lot of Americans still probably think they invaded Iraq because Saddam Hussein was behind 9/11. You can sell anything to Americans if you're convincing-enough... as Trump himself learned.
But, yeah: President Pence by 2018, I imagine. And, because the Republicans looked like idiots, the Dems will take a lot of seats in the midterms and maybe get at least one house of Congress back.
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* When I was a kid, we had a toaster that often didn't pop back up on its own when the bread was toasted, so if you didn't keep an eye on it, the bread could catch on fire. My mom was on the phone with the contractor who was going to build an addition on our house, and she'd forgotten about the toaster... which now contained flaming bread. She very calmly told the guy on the phone, "Sorry, Bob, my toaster's on fire, I'll call you back." She then unplugged the toaster, sat it in the sink, and opened the window to let the smoke out... and called Bob back, of course.