There is an endless amount of misinformation about who becomes President in the event where the sitting President is impeached or is no longer to perform the duties of the President. The Rules of succession are actually pretty simple and if Trump is somehow removed from office, although that is certainly unlikely, we may see the Supreme Court battle of the Century. 

As things are now, after Trump the Vice President would take a seat in the Oval Office. Common Knowledge suggests that Nancy Pelosi, the Speaker of the House, would take the office next… but this may not be constitutional or even logical. 

In the constitution, it states that Congress will designate which Officer comes next. Note that Officer is capitalized, this is very important in the constitution. This term, Officer, is used to describe officials who have been appointed to a cabinet position. This being considered, the Speaker of the House is not the one who would be appointed to the office of the President in the case of the removal of the President and the Vice President.