About ninety percent of what gets done on a day-to-day basis is done by the professional bureaucrats, and for the most part, they just keep doing their jobs, relatively competently  though not often imaginatively, regardless of who the President is.

Foreign policy is largely handled by diplomats. Trump doesn't have a large acquaintance of intellectual ideologues so he'll appoint his business cronies to places like the Court of St. James and professional Republican diplomats to key embassies like Moscow. The diplomatic corps will realize that the diplomatic thing to do is reassure world leaders that the tweets coming from Trump Tower are entertainment, not policy.

A lot of bad stuff is going to happen. Medicaid will get stomped and a lot of poor people will suffer and die unnecessarily. But that would have happened even if it had been Cruz or Jeb! There won't be a trade war with China and we won't withdraw from NATO. The next four years will be conservative-bad,  not lunatic-bad.