Well, as for the first - that tends to change from skill challenge to skill challenge. It might involve a day spent traveling around town asking questions, or it might be a 5 minute ritual to converse with spirits, or it might be having some players fiddle with a golem control panel during combat, while the others keep them safe.
My goal is usually for skill challenges that don't feel like they are overriding other activity, but I have also had success with more transparent skill challenges. The first scenario is how I tend to run challenges in LFR adventures - usually, the goal of such challenges is to find out some information or accomplish something over a period of time. Rather than going around the table and having people make skill checks one at a time, I will have the group RP their way through the scenario, recording skill challenges as they are made, and going from there.
I tend to let the players come up with their plans first, but will usually provide possible approaches (ie, appropriate skills) if they are stuck. And I've had great success with this method, including several adventures where some players never realized they were in a skill challenge at all! Letting it provide a framework to determine success without having it impose upon the roleplaying itself is perhaps the most valuable element the skill challenge system offers.
I've also run more complicated skill challenges where I've tended to lay out on the table exactly what the PCs can do as part of it. I use this generally for scenes that I want to feel big and cinematic, but want to still move through in a pretty brisk timeframe. My most recent example involved the party, having acquired a magical artifact in the elemental chaos - and incurring the wrath of a primordial in doing so - now needed to flee to a portal to the Feywild (on the back of a friendly magical Roc), break through the enemy lines on the other side of the portal, and get to the place they could use the artifact to save the day.
What I decided was that there would be several 'turns' of the skill challenge - the first few involving fleeing the primordial's ice storm and driving off the elementals he sent to chase them down, then a round spent escaping through the portal (which would be sealed by a wall of ice), and then avoiding hurled boulders and other attacks from an enemy army as they get to their goal. Each round represented a solid chunk of time - maybe a few minutes, maybe hours fleeing across the ice.
I took an idea from one of Mike Mearls extended skill challenges, which was that if a PC spent their skill challenge 'turn' attacking enemies, they got several rounds of in-combat actions with which to do so. I didn't bother with a battlemat, just assumed PCs would be able to freely line up attacks as desired, since giving the time-frame involved, enemies would constantly be moving in range of their attacks. I used simple to track enemies (two-hit minions, essentially).
PCs that weren't actively fighting could do a variety of things. Some of them were ones I had accounted for in advance - using Arcana or Nature to help drive off the storm assaulting them, using skills to help heal the Roc or let it evade enemy fire, etc. On the other hand, some of them came up with their own clever ideas - one player wanted to expand a daily item power that would let him turn invisible, and instead try and briefly extend its power to cloak the entire party from the storm. Not something I accounted for in advance, but I let him try an Arcana and Stealth check to pull it off, and it made for a very memorable moment.
SInce it was a long challenge, and I wanted to encourage PCs to be using powers in the midst of it, I featured a milestone in the middle of it, and allowed their success at the end to give them various bonuses/recharged powers as it dumped them into the final battle of the session. Some still just held onto combat powers for combat, but others were pretty creative - such as the Stealth check Invisibility mentioned above, or a Warden using several plant-growth creating powers in interesting ways. I don't have hard and fast rules for the use of powers in creative ways, but I tend to encourage it, tend to use Keywords and resource as an easy way to figure out what can be done with the power, consider its resource level (Encounter vs Daily) to figure out how powerful an effect it can produce, and usually still require a skill check if they are being used in an unusual fashion. If a power would simply naturally produce an effect that would work in place of a skill check - using a Teleport power to get onto a roof instead of an Athletics check, for example - I might simply count it as an automatic success. Rituals would be addressed similarly.
All in all, this was a pretty big event, but it allowed me to have a big, epic scene that the PCs could all shine in, without having to simply run it as a series of encounters or just sit there describing things to them. That blend of action and narrative is really what I feel skill challenges are all about. Ideally, entirely on their own, players can come up with what approach they want to take to solve a problem. In an earlier edition, I might just decide whether or not that approach works, or try and come up with a way to run it on the fly. With a Skill Challenge, I have a simple set of guidelines I can extrapolate to figure out their success or failure.
The danger, of course, if that if the PC feels forced into rolling a skill they don't want to, or wants a more direct solution (bash people's heads in), a skill challenge can feel like a straight-jacket. Or if they have a creative solution the DM doesn't want to let them use, or if they fail a check and get upset at seeing the results of failure without another chance to try again - there are a lot of potential pitfalls. Which is really why I try to let the players drive the challenge, and try to keep them seamless with everything else going on, rather than suddenly have them feel like they've been shifted into 'skill challenge mode', and playing a button-pushing game rather than an RPG.
The key to realize is that the fundamental action a player is making during a skill challenge shouldn't be rolling the dice for a skill check, but instead making a decision for how their character will be trying to succeed at the current task. Too many skill challenges focus on the check itself as the key element - the check is simply something that helps evaluate their success. Making sure the focus is on the decision itself, and what their character is doing - focusing on that is the key to a good skill challenge, more than anything else.
The truth is that I certainly don't have an elaborate formula for plotting out all these rules - I've considered it, but found that the guidelines from page 42 simply make for a great starting point, and anything beyond that can be figured out on the fly. It does often come down to DM call, but in ways that helps the fluidity of the situation, and hearkens back to the atmosphere of trying crazy things in earlier editions, as well.
And... hopefully that at least helps with the 'more details', since I've definitely rambled on for quite a bit. There is a lot of good skill challenge out there already, both in Dragon Magazine, the DMG and DMG2, and numerous independent blogs. But it really is an art in many ways. I consider it one of the areas of 4E with the most potential, but also the area filled with the most potential pitfalls for both the DM and the players.
