I skipped right over 3rd and 4th editions, but have just learned about skill challenges.
I've read the applicable section in the 4th edition DMG. I have a bit of an idea how I might use them in my game. But they seem to rely on a player saying "I'll use diplomacy" or some such, instead of just telling the DM what he's going to do and letting the DM call for the specific Skill Check. That is, without the guidance from the DM saying "you need 6 successful skill checks among these three skills..." players may be floundering for what they should do.
From the 4e DMG, p 74:
Begin by describing the situation and defining the challenge. . . . You describe the environment, listen to the players' responses, let them make their skill checks, and narrate the results. . . .
In a skill challenge encounter, every player character must make skill checks to contribute to the success or failure of the encounter. . . .
Sometimes, a player tells you, "I want to make a Diplomacy check to convince the duke that helping us is in his best interest. ' That’s great - the player has told you what she's doing and what skill she's using to do it. Other times, a player will say, "I want to make a Diplomacy check." In such a case, prompt the player to give more information about how the character is using that skill. Sometimes, characters do the opposite: "I want to scare the duke into helping us." It’s up to you, then, to decide which skill the character is using and call for the appropriate check. . . .
It’s also a good idea to think about other options the characters might exercise and how these might influence the course of the challenge. Characters might have access to utility powers or rituals that can help them. These might allow special uses of skills, perhaps with a bonus. Rituals in particular might grant an automatic success or remove failures from the running total.
The main job of the GM is to manage the unfolding situation - you have to narrate the consequences of checks (even successful checks) in such a way as to make it clear
why the situation has not yet resolved. If that's not clear to the players, then they don't know what it is that their PCs are trying to achieve.
The main job of the players is to engage the situation. This should involve explaining what their PCs are doing. Some of the time the appropriate ability/skill check will be self-evident. If not, it's up to the GM to adjudicate (presumably most GMs will do this in collaboration with their players).
Here's a link to an actual play report of a social challenge (in 4e). And
here's a physical one.
Don't use skill challenges as written, because they are awful. They've got a massive amount of variance based on the DC and skills of the PCs, and the best possible plan for dealing with them as a player is to make sure that only the person with the best relevant skill participates (either by withdrawing from the situation, or by always "assisting"). They're also pretty tedious dice rolling affairs.
Anyone who is interested in using more formal non-combat resolution (which after all is in principle no more mysterious than formal combat resolution!) needs to address these points.
Dice-rolling: action resolution in D&D often involves dice-rolling. It is the GM's job to give some sense (either explicit, or implicit in the narrated situation) of what will happen if the check succeeds or fails. It's the player's job to martial resources (eg spells, items, other abilities) to manage the roll and tilt the odds in his/her PC's favour.
"Best relevant participant": D&D is played mostly as a group affair. In combat, we don't typically allow the fighter to duel the hobgoblin captain one-on-one while the other PCs look on. The GM takes steps to make sure all the PCs are involved. Non-combat resolution needs to be approached similarly. Eg the NPC asks the CHA 8 fighter, "So, what's your opinion on the matter?" Either the PC says nothing (looking foolish, and costing a failure) or the player rolls the dice. (A CHA 8 fighter is no more
entitled to never have to talk than a low AC, low hp magician is
entitled never to be attacked in combat.)
Variance: 4e offered various formal and informal ways of managing this, the most sophisticated being in a combination of DMG2 and Essentials. The 4e maths will have little relevance to 5e, but my gut feel is you'd want the typical DC to be 10 with the occasional 15, perhaps growing to 15/20 at upper levels. My maths suggests that a 75% uniform chances of success per check gives around a two-thirds chance of getting 6 successes before 3 failures. At 1st level, DC 10 should give typical chances of success around 75% (+2 from stat, +2 from prof is enough) - and players can use inspiration and other sources of advantage, buffs etc to improve on that.
If you use higher-complexity challenges at these same DCs, the players will need to work much harder to succeed (eg more spells or similar abilities to substitute for checks, more advantage, etc; 4e Essentials offered a different way of managing these higher-complexity challenges, something like a skill-challenge specific inspiration variant, but it's a bit clunky and I would't really recommend carrying it over to 5e).
A skill challenge a great DM tool to add another layer to the game that did not exist in the past. It makes you think beyond just monsters, traps and ad-hoc role playing. The hard part is making it transparent and placing it seamlessly into the setting
As a practical bit of advice, here is a useful thing I learned from [MENTION=6696971]Manbearcat[/MENTION]: when the skill challenge starts, set up a die of the appropriate size for the number of required successes, which counts up as the challenge is progressed through; and a die to record the failures (I don't have a 6-sided die marked as a d3, so I just use a d4 with it starting at 4 for zero).
I find that this helps reinforce and focus the narration, so the players have a sense of how much is still at stake, and hence can make better decisions about the deployment of resources.
EDIT: I thought maybe I should post the maths in a spoiler block, for verification purposes:
[sblock]Chance of 6 successes and no failures = .75 ^ 6 = approx .18
Chance of 6 successes and one failure = (.75 ^ 6) * (.25) * (number of distributions of 1 fail within the first 6 rolls, which = 6),
so equals .75 ^ 6 * 1.5 = approx .27
Chance of 6 successes and two failures = (.75 ^ 6) * (.25 ^ 2) * (number of distributions of 2 fails within the first 7 rolls, which = 21). This = approx .23
So the overall chance = approx .23 + .27 + .18, which is just a touch above two-thirds.[/sblock]