DnD 4e is based on tactical combat on a grid. Yet when I read the dungeon master's guide, I saw skill challenges for situations that don't seem to require a grid. For instance: Urban Chase. The players are after somebody and must make a series of roles to see if they catch up with the person. They require 12 successes before 6 failures. The challenge is obviously not meant to be done on a gridded map. But I really am not sure on how to conciliate this with the structure of the rest of the game. How can I get my players to transition out of a grid situation, then back in? How can I satisfy the expectations of my players, who were promised an epic chase and got a series of dice rolls instead?
D&D 4e only uses a grid for tactical combat. Roleplaying and skill challenges don't need a grid, so you simply don't use one.
Here's an example. After a dungeon crawl, the players return to the local town to buy food. While they're there, some of their gear gets stolen by bandits. The players chase them down, using opposed skill checks that make sense in context (any form of riding, endurance, or even Constitution checks all work, although there are probably a lot more that you can use in your game - it depends on your players and their characters), and finally fight them. This is when you put down the grid. After the battle, the players learn that the bandit lair is hidden nearby with treasure inside. They have to complete a skill challenge to find it, using a variety of abilities. You don't need the map for this, so you put it away again. The players then do the challenge. They receive treasure and experience, and return to the town, ready to re-enter the dungeon.
To make skill challenges interesting, you need to narrate them so they seem gripping tales of superhuman effort rather than a string of rolls. Consider the chase from earlier. You can either say "The bandits roll a 12 for Riding(Land-based), plus their modifier of +5. You've got a 14 and a modifier of +7. Ok, you've moved closer", or "The bandits manage a 12, pulling out ahead of you. You can see the lather on their horses as they are driven near exhaustion, but the skilled riders coax a little more speed out of their mounts. Oh, 14, nice! You lean into the saddle, wind rushing through your hair, and are rewarded by the sight of the bandits coming ever closer. They look back and see you, and begin to curse."
Moving out of grid-based play and back again is something you shouldn't have to do. You and your players use the grid to get a better idea of where they and their opponents are, as well as the general shape of the room. But play is more exciting if you (and they) narrate actions as well as describe them mechanically. "I Bull Rush the Kobold leader" is an option from a menu. "I Bull Rush the Kobold leader, sending the both of us skidding along the floor" is interesting. If your players get used to using grids as tools, rather than as a gameplay mode, they will have an easier time going between using the tool or not. They should eventually be able to determine themselves whether they need a map or not, and pack it away on their own when they recognise it's no longer needed.
Skill Challenges, are, sadly, one of the worst designed parts of 4E. We saw them do some math changes to the way they work over the course of 4E and also never really gave enough advice on how to run them well. I've written a guide to Skill Challenges over here. (and even more, here.) The short, salient points:
Only use a skill challenge if it would be the equivalent to a major scene in a movie or a videogame level - don't use it to do things like, "open a door" etc. Use it to sneak into a castle, not to sneak down the hall.
Fiction First. Give modifiers based on what the players describe themselves doing. Smart or clever ideas should be a bonus. Weak ideas are a penalty. If you are willing to bend the rules a bit, some actions should be auto-successes or auto-penalties based on your judgment. It should be a rare time you roll the dice raw without modifiers based on the description.
Making each roll worth something. If you win the challenge but had 2 failed rolls along the way? Those 2 failures should still hurt or cost something. Maybe you lose or damage some equipment or supplies, or lose a Healing Surge in exhaustion. If you lose the challenge but got 3 successes, those 3 successes should still mitigate/help along the way too - maybe you gained some information, picked up a tool, or otherwise found something useful.