I don't say "it's a skill challenge", just like I don't say "it's a combat". For skill challenges the players usually get what the problem to be solved is and try to solve it telling me what they are doing and so forth. I will give them feedback and ask for skill rolls.I strongly agree with this.
I'm less sure about this. I generally do let my players know they're in a skill challenge, especially if its of high complexity, because otherwise they don't have all the information they need to make sensible choices about how to use their resources (like powers, items etc).
I usually don't roll for initiative in skill challenges, but ask the players what they are doing, running it a bit more freeform than a combat. If a player doesn't do anything, I usually ask them what they want to do and allow the players to jump in when they get a good idea.
The point of the above is to make the game flow from pure role playing to a skill challenge and back to role playing without the players really noticing, making the game experience more immersive.