Follow-up question to Where can I find actual play examples of skill challenges?
The Dungeon Master's Guide 2 on pages 80-81 has an example of play of a skill challenge. The DM just describes the situation, and the players without further prompting and one after another all either propose a skill to use or propose an action that is easily identifiable as a skill check. Furthermore they all propose skills that apparently were foreseen in the list of primary skills for that skill challenge.
Given that real players don't act like that, how do I actually run a skill challenge? Dividing that into sub-questions:
1) At the start of the skill challenge, if I don't tell the players that this is a skill challenge, they are likely to mostly propose role-played actions that are hard to translate into a skill check, e.g. shouting out "Hold the thief!" in a crowded market instead of using Acrobatics to run after him. So, what rules do I tell my players? (opinions on that seem divided, see Should I announce to the players they are in a skill challenge?)
2) In response to a general "what do you do?" prompt, some players are more likely to answer than others. Should I impose rules that ensure that every player gets a turn in the skill challenge and participates? (see Should I take turns during a skill challenge?). Related to that, how do I handle player input that uses "we" instead of "I", e.g. "We run after the thief"?
3) How do I handle ideas which I like from players, but which don't really correspond to a skill? Like in the example above, shouting "Hold the thief!" sounds like a good idea to stop a thief from running away in a city. But it would translate badly into let's say a Diplomacy check, especially if the character isn't skilled in that.
4) What if somebody proposes a good idea which corresponds to a skill that isn't listed in the primary or secondary skills for that skill challenge?
5) Already partially answered elsewhere (How do I work Powers into Skill Challenges?), what do I do if the players want to cast spells instead of using skills?
6) Once the initial spontaneous idea have gotten used up, how do I prevent the players from simply checking their character sheet for their best skills and just proposing those? Even the DMG2 example of play has players just proposing "Can I make an Arcana check to see if I know anything about it?".
In summary, I would like to know how I as the arbiter organize the typically somewhat chaotic responses of my players into the rules corset of the given skill challenge, especially if that skill challenge comes from a printed adventure module. Please note that I am asking how to run a skill challenge within the rules of 4th edition Dungeons & Dragons. I am aware of alternative systems like Obsidian