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.
The early system - n successes before n failures - was broken, it actually got /easier/ to succeed at an SC the more 'complex' it got. The first errata changed it to a more fundamentally workable n successes before 3 failures, and the final version (Essentials Rule Compendium) was pretty decent. It could be
easily adapted to any d20 game...
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.
I've run SCs without even telling the players they were in one, and by coming out and telling them the key skills & how they might be used (but also pointing out they can try anything they can think of). Both can work, as can things in-between, it really depends on the challenge you have in mind. I've also had and seen some great successes when expanding a Skill Challenge into a sort of mini-game in itself, especially for more abstract things (one example was a political campaign), or where progress can be tracked visually (as in a race or chase scene).
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.
Laying out the Challenge in the open could work quite well in 4e, with its greater player focus. In 5e, though, I'd tend to go to the first option I mentioned above, and not even revealing they're in one.
Is there a good way to use skill challenges while keeping the "just tell me what you want to do" aspect of playing D&D?
Yes! They make a fine behind-the-screen tool for the DM. Just describe the challenge that confronts the PCs, and let the players describe what they're doing to overcome it. Call for checks from each player and don't hesitate to use group checks when everyone's pitching in. Keep a tally of successes vs failures. Be sure to have in mind a minor consequence or setback for the first two failures, and think about what interesting forms failing the challenge might take.
One thing to note: 4E was huge on player empowerment.
It was, but 3e (and even late 2e) were too.
They wanted players to declare their action and do it. Not wait for the DM to give them permission to do it, or wait for the DM to resolve their action.
Not so much. 4e rules were written pretty clearly, so DM adjudication wasn't often necessary, and it did play well 'above board,' which allows the style you describe, but doesn't in any way require it. 3.x was prone to a similar phenomenon because of the general reverence for RAW. But in both cases the main impetus was just finally /having/ skills. You could actually decide what you PC would be good at, which was a huge step up from early D&D, when you had only random stats and DM judgement to go on.
"if it says you can do it, you can do it." with a DM taking a more reactionary posture to what the player just did, instead of a prescriptive posture in determining what was allowed to take place. I understand this is a big divergence from earlier editions.
It was not. There have always been rules lawyers who expect to be able to invoke a rule and have it work as written. 3e was a big step forward in that there were a lot more rules a player could specifically invoke, and that knowing them well (system mastery) could deliver a big advantage. If anything, 4e pulled back from that.
5e really pulled back from 'player empowerment' and 'returned' to DM Empowerment. But, it's one of those returns that's aiming for an idealized extreme of how a perceived golden age was, rather than for the muddier reality of 'early D&D' which was highly varied from DM to DM. FWIW.
You seem to be assuming that 4e flat out said you can do certain things regardless of DM opinion or disapproval. That is not at all the case, and it's not how 4e (or any other edition) has worked.
True. And it can't not be true, because nothing a rule book can saw or a designer can do could keep a given DM from changing things.
However, 3e & 4e created an expectation that the DM would respect the rules. Neither entirely on purpose, but both quite dramatically compared to older editions.
3.x came right out and articulated Rule 0 - then forgot about it, and presented bushels of player options. The result was a community that enshrined RAW and an attitude of entitlement that, if you got a supplement and picked an option, you should be allowed to have it, and it should work as written. Many of us resisted that (in the end, I only ran 3.0 for about six months and almost exclusively approached 3.x as a player thereafter), but it was the overriding climate at the time. One of my perennial frustrations with gaming in general became particularly pronounced in the 3.x era, IMHO: the player declaring a roll and calling out the result - with the expectation of a big number guaranteeing success.
4e was subtly different, in that system was better balanced & more clearly presented, so there wasn't this impetus to use the RAW because you could manipulate it for an extreme advantage, nor to have cutting debates about which interpretation was really As Written, but merely to use the rules as-is because they mostly worked.
5e gets completely away from both other modern editions in being strongly DM-focused. A player really shouldn't call out a skill and make a roll, because it's the DM's place to call for checks and rule what proficiency might apply and set the DC. There's very few tables of DCs for a player to familiarize himself with. No 3.5-style Diplomancer build, not because you can't optimize for a fairly high CHA check, but because there's no fixed DC for making an openly hostile gnoll into your helpful new friend.