I live in the South, where door holding is expected and is always acknowledged with a "thank you".
The exact etiquette is a bit of a judgement call. If the person is far enough behind that you can enter and the door will close before they reach it, you don't need to hold the door (although you can). If someone is right behind you, you hold the door open from the outside and allow them in first. If the distance is such that you can enter but they will reach the door before it closes, you hold it ajar behind you so that they can grab it from the outside and keep it open for themselves while they enter.
There are definitely cultural norms for holding doors. When I travel north and exhibit my Southern manners, people often look at me like I'm crazy. Watch how the natives behave and follow their lead.
I'm in Australia, and this is how I handle holding doors. I'm perfectly happy to walk through a door held open by anyone, and happy to hold a door for anyone.
Same here, but I will hold the door continuously for old people, people with prams or those with lots of bags.