It's axiomatic that the DM is responsible for describing their world to the player characters. And it's an area where I've seen many DMs, including myself, struggle for consistency.
When I examine the first sentence I wrote, which I doubt any one disagrees with, I see that one of the reasons I've struggled with consistency is the way I've traditionally phrased it. Looking at it the way I would look at a business requirement for designing an application, my response to the author would be, "OK, so what? You haven't actually provided any requirements, just a vision statement. A good requirement is when X occurs do Y, all you have given me is the Y." So that gives me a starting point for my analysis, define the Xs, i.e. what occurs during play that triggers the DM to communicate with the player characters.
First and foremost is describing the environment in response to character actions. They open the door what do they see? Do they find the secret door? What monster is trying to melt their faces? The answers to environmental questions are handled by the mechanics of the game and only need a little fleshing out. 'It's a 10x10 room' is a boring description, fleshing it out to 'it's a 10x10 room with a water stain in the far left corner' can be done on the fly or set up in advance with any number of random dungeon dressing tables. Fleshing out descriptions adds depth to the narrative and engages the players' interest. Similarly, you should avoid 'You found a secret door', instead let them find the trigger, but describe it in a way that keeps the players in suspense while prompting them to on what actions are available. 'You found a hole the size of your finger in the wall, are you going to poke it?' If they respond, 'I'm checking it for traps', the response could be 'The back of the hole gives way to your probe with a click, and a section of the wall slides open' or you might say, 'There's a snap and your probe comes out shorter than it went in'.
The second trigger actually occurs first, background information and house rules at the start of the adventure. Sometimes derogatorily referred to as 'fluff';background information provides the players with common knowledge the characters are expected to have - like when the society has a penchant for burning witches,informs the players of the initial goals the DM is prepared for the characters to pursue and may assist the players in developing motivations for their characters. The actual amount of background information may be limited to "I'm going to run a meat grinder funnel. Roll up a dozen characters and we'll see who survives." On the other hand, the background information on Forgotten Realms runs to hundreds of pages, not counting the hours of semi-canonical game play.Even when I run a campaign set in the Realms, I provide information on the starting area and any character restrictions. I also make sure to provide a teaser of what the first adventure will be, after all I don't want the players to expect a standard dungeon crawl if I'm preparing to have them doing second story work in the city. In regard to house rules, I try to start by accepting anything from the core rule set (regardless of system), but splat book additions need my approval on a case by case basis. I've seen some discussions on the RPGBA boards about "safe words" and codes of conduct this year; neither of which has a place at my table. If your character is an a-hole, it's my responsibility to deal with it in game. If you are an a-hole, I'll let you know and I expect you to feel free to inform me when I am one. If you are too fragile a blossom to speak up for yourself,don't sit down at my table.
The third trigger for DM communications is PC interactions with NPC's, whether it's the barkeep or the goblin guarding the cage, this is where the term role playing comes from. I do find it hard to do characters and I need to improve prompting my players to be in character themselves during these interactions. When the roles are stripped out of the interactions, I find a lot of the fun of the game goes away too. As far as the types of information NPCs impart traditionally it has been rumors, but John Arendt over at Dreams in the Lich House had a couple of good posts on Campaign Events last month. I like the idea of using campaign events to give the world a feel that there is more than just the town and dungeon and that the characters are not necessarily the biggest fish in the pond. As far as rumors, well that's a topic for another post as there is a lot that can be done with them.