4e DMG pp 72, 74:The problem is skill challenges are designed with action resolution in mind rather than actually describing the problem in question and leaving it to the players to solve the issue.
Define the goal of the challenge and what obstacles the characters face to accomplish that goal. . . .
Begin by describing the situation and defining the challenge. Running the challenge itself is not all that different from running a combat encounter (see Chapter 3). You describe the environment, listen to the players’ responses, let them make their skill checks, and narrate the results.
4e PHB pp 179, 259:
Whatever the details of a skill challenge, the basic structure of a skill challenge is straightforward. Your goal is to accumulate a specific number of victories (usually in the form of successful skill checks) before you get too many defeats (failed checks). It’s up to you to think of ways you can use your skills to meet the challenges you face. . . .
In a skill challenge, your goal is to accumulate a certain number of successful skill checks before rolling too many failures. Powers you use might give you bonuses on your checks, make some checks unnecessary, or otherwise help you through the challenge. Your DM sets the stage for a skill challenge by describing the obstacle you face and giving you some idea of the options you have in the encounter. Then you describe your actions and make checks until you either successfully complete the challenge or fail.
Chapter 5 describes the sorts of things you can attempt with your skills in a skill challenge. You can use a wide variety of skills, from Acrobatics and Athletics to Nature and Stealth. You might also use combat powers and ability checks.
In other words, the GM describes