I am completely new to DMing and I am considering including a skill challenge in my next game. Most of the players are new to 4e and one of them is new to D&D in general. Should I explain to them the details of a skill challenge, or just roll with their role-play and ask them to roll skills as appropriate?
I had success doing the following while refereeing anything involving skills or abilities.
In short describe, make a ruling, and roll.
I personally don't mind feedback from the players. Often they think of things I don't. So after I tell them how it going to be resolved I will listen to what they have to say and make any changes I feel is warranted. But in the end the final decision is up to me.
Specifically 4e Skill Challenges often involve multiple steps and rolls, so you may want to make it more interesting by doing the roleplaying for the few rolls and if there is impending failure have the players figure out an alternative to the remaining rolls. Again the same describe, make a ruling, roll steps apply.
I can't stress enough how always making sure that the players describe things as if they were there before rolling is important for roleplaying. For me as well as the players. Often it leads to interesting details being revealed and enhances the encounter.
Definitely tell them that they're in a skill challenge, or if they're about to take an action that would initiate a skill challenge. You wouldn't withhold that they're in a combat, would you?
I would also summarize what the potential outcomes are, in a general way. Example, best case: the miners will help you go spelunking; worse case: they don't want anything to do with you, but will grudgingly sell you equipment at twice what its worth.
If you're dealing with new players, give an outline of how skill challenges work.
Short answer: Don't tell them they are in a skill challenge.
I would say, just let them tell you what they want to do, and think of skill checks to suggest for them to roll. If they don't realise they should be rolling a skill, just let them know "you can use skill X to do Y". Don't tell them outright that they are in a skill challenge - it breaks immersion.
Optional: If you want to make it more close to roleplaying, and would rather not tell them to "roll skill X" (which is a wonderful idea) then ask them how they deal with the situation at hand and decide which skills are better suited to what they describe, and roll them yourself in their stead, adding their bonuses, of course (this is just an idea, you might want to do it, you might not, I am not saying this is the best way to do it, it's only optional) and at the end of it, you can choose to inform the players you rolled skill X for them, or not inform them, up to you. (keeping immersion in mind)
There are some excellent questions around skill challenges on this site:
I'd suggest reading through those; some of the most salient points though.
Once you know what sort of skill challenge will be, figure out how player might react depending on whether you announce it, or keep it secret for a while. When you (think you) know how players will react, plan accordingly, picking the one they will enjoy the most.
Ultimately it's down to you, and the individual challenge and players involved.