I'm having the same problem, I've asked so many people but no one have told me exactly what to do. Talking about the dailies
Specifically, you have to begin questing in Mount Hyjal. If you haven't begun questing there yet, then you can pick up the "Hero's Call: Mount Hyjal!" quest on the Hero's Call board in any of the major cities.
You can also skip the Hero's Call board quest and go directly to Moonglade. Talk to the NPC called Emissary Windsong, and she'll offer the quest called "As Hyjal Burns". Accept that, and start questing in Mount Hyjal :D
You don't have to complete all the quests in Mount Hyjal to unlock access to the Firelands daily quests. You only need to complete quests to the point where you've reclaimed the Regrowth area. You'll know when that is, as there'll be a little cutscene that shows it (don't want to spoil it :P).
(but it's perhaps worth saying that it's advisable to complete all the quests in Mount Hyjal, as certain characters won't be visible in the Firelands if you haven't "unlocked" them through the Mount Hyjal questing experience)
Anyway, once you've done that, then the quest "Guardians of Hyjal: Firelands Invasion!" will be avaliable from the Hero's Call board in any of the major cities. Once you pick that up you're effectively doing the new quests. It's just a matter of progressing from there, by doing the quests as they're offered to you :)