It has been a bit of a re-learning curve after C5:BNW, but basically I settle cities now until I run out of convenient space, or I just get tired of escorting Settlers and start using my troops to take other peoples cities instead.
I often also have to build cities hella-far away from my capital as I go up the tech tree as I have yet to have a game where, when I generated the map myself, I had any strategic resources anywhere near my start spot. If Iron even exists on my starting continent I tend to consider it a miracle at this point, so that alone has driven me to a very wide spread, far-flung habit of empire building.
It also varies based on the victory condition I am going for, in particular the Tourism (refuse to call it Culture) and Religion victories. Both of those are so heavily dependent upon Theatre / Holy site districts that pretty much the fastest way to win is to build as many cities as you possibly can, as early as you can, and get the districts out earning GPP / Faith so you can produce Great Works / Apostles. So those victory types tends to encourage me to build more tiny cities that I never plan to have grow past size 5 or so, just to get those districts churning out the points needed for victory.
With Entertainment Districts being relatively early in the Civics tree and (except for Kongo) Neighborhoods being later, I tend to find that Housing far more then Amenities limits my growth and keeps me from getting myself into too much trouble from expanding myself into an imperial implosion.