He wins when he wins; He wins when he ties; He wins when he loses. It’s time to admit that we are playing his game by his rules.

This is the original textbook definition of an internet troll. The meaning has changed some since so many people use the epithet troll or trollng to mean a lot of different things. But from experience as a moderator circa 2003-2004 (when in addition to increased descriptions of the syndrome on the internet, trolls confessed their motives to me in private messages)  I could recognize the original techniques the first week of his presidency, and he's increased his trolling a great deal in the following months.

The remedy is simple on the internet: don't feed, ignore. It is a disease, getting an emotional rise out of people gives them a high, when they don't get that, they move on and try someone else. But I don't know how you do that when the troll is the President. The New York Times or Congress cannot like, decide not to feed...

Edit to add: A secondary technique that has proved to work with some internet trolls is ridicule. You are not giving them the emotional reaction they want, you don't respect them enough to get upset, to start seriously arguing and debating. In the case of Trump, I notice some foreign leaders are doing this. In the case of a President, I think it must come from peers, so that might work some.

With him and the media, though, it's more complex. Because for decades, he considers himself an expert at manipulating the media along the lines of P.R. (Like many have noted, it almost seems sometimes that he would rather be White House Communications Director than President.) So even though they must keep awareness that he might consider "all publicity is good publicity", if the media is truly going in the direction he does not wish them to go (example: constant coverage on Russia collusion), then they are doing the smart thing. And frustrating him, and he doesn't know how to react.  But if they are giving him coverage along the lines of "liar in chief", that is just giving him more attention that he wants. That is, he is able to get a rise out of them with outrageous statements and lies and smears. Getting a rise out of people and getting attention is the point, the only point.