What it says
It's Chapter 3, "Combat Encounters," starting the section on "Actions the Rules Don't Cover."
Your presence as the Dungeon Master is what makes D&D such a great game. You make it possible for the players to try anything they can imagine. That means it's your job to resolve unusual actions when they players try them.
The first suggestion is relatively tame: if it's just a favourable situation, give the players a +2 on their next roll, or combat advantage. If it's a sucky situation, give them a -2. Same old +/- 10% you can find in any other RPG.
The next suggestion is where the slippery slope starts:
If a character tries an action that might fail, use a check to resolve it. If the action is essentially an attack, use an attack roll. It might involve a weapon, and target AC, or might just be a STR or DEX check against some AC/Ref/Fort defense. Use an opposed check for anything that involves a contest between two creatures.
So far, so good; the 4e DMG is the "Dungeon Mastering for Dummies" book you've been reading up until now. Now get ready:
If the action is related to a skill... use that check. If it is not an obvious skill or attack, use an ability check. Consult the Difficulty Class and Damage by Level table below and set the DC according to whether you think the task should be easy, hard, or somewhere inbetween. A rule of thumb is to start with a DC of 10/15/20 for easy/moderate/hard and add half the player's level.
Here's where the fun begins.
The above quote is so vague that we still can't agree as to what the hell they meant. 3.5e fans interpret it as meaning that DCs continuously increase at the same rate that they gain bonuses to those checks, i.e. an action that required a roll of 10+ at level 1 will always require a roll of 10+. 4e fans argue that the whole chart is just a suggestion to make eyeballing DCs a little easier for the DM. A few retards even decided that this means that a check that had DC 10 when they found it at level 1 will now be DC 14 when they try again a few levels later. These guys are probably trolling and should be ignored.
The rest of the page explains the reasoning behind the damage values, which are roughly equivalent to a typical attack or power from somebody of that level. This part is pretty innocuous so nobody cares about it.
- To 3.5e fans, this basically renders levels meaningless since the DCs just keep rising arbitrarily as you get stronger.
- To 4e fans, this is basically just the same scale 3.5e used for most DCs, but with less eyeballing.
- Every now and then some chucklefuck asks "how is this different from Rule Zero?", which starts an even nastier argument.
The problem comes from trying to express an abstract idea in a mechanical way. Obviously, there needs to be the possibility of failure for challenging tasks to create a sense of tension. But the players are heroes, and as such tend to get really good at things, and a lot of things that would be 'hard' to a novice become trivial to them. So the idea of 'easy/medium/hard' really means 'easy by the standards of the character at this point in their development'. And that's where the problem comes from people thinking it is an absolute scale of difficulty rather than relative. The designers framed things in a way that seemed reasonable, so that leveled up characters don't just breeze through everything and there remains the important sense of dramatic tension, especially important for dealing with checks that happen against a time limit (pick the lock before the monsters catch up!) and because the numbers are in your face obvious people complained about a number treadmill.
In the "official errata to the Dungeon Master's Guide" (July 2008). They lowered the difficulty classes for Easy/Medium/Difficult to 5/10/15 with +1.5/+2/+2 per 3 levels. This doesn't actually fix the real problem here, and actually makes it worse (now the effective DCs rise every level). You're best off just ignoring it.
The Ultimate Question?
Some people who notice the page number realize what is the true ultimate question.
Q: What will make the most fa/tg/uys rage?
A: Page 42