First, there are these new X-Men: Days of Future Past stills via Empire. This is concrete stuff, real scenes from the movie, etc.
Then, there are these rumored plot points via Comic Book Movie which are very much less concrete.
Maybe I just find them dubious because one of them is one I very much wish were true but refuse to get my hopes up about. But take these with a giant grain of salt, while at the same time heeding this SPOILER WARNING to read on at your own risk. I mean it. There's some big reveals in here. Don't get angry with me if these all turn out to be true and you wish you hadn't known. Maybe bookmark to read after you see the movie, just in case.
Young Jean Grey appears in the past.
Cannonball appears in a mutant refugee camp in the future that is attacked by Sentinels.
Rogue has been captured so the Sentinels can duplicate her powers and use it against mutants. The X-Men later rescue her, and, due to the genetic manipulation done by the Sentinels, Rogue briefly displays super-strength and flight during the escape.
The Sentinels are made of magnetized plates and therefore can change their shape, becoming learner or bulkier. The addition of Rogue's powers makes them virtually unstoppable, which is why the X-Men decide to move forward with the last-ditch effort to change the outcome of the war by altering the past.
There is a mutant unit led by William Stryker that Havok and Toad are a part of, in 1972.
Banshee left the X-Men to be with his family, and Emma Frost has been captured by the government again, but Magneto isn't bothered to break her out yet again.
Mystique assassinates President Kennedy while Magneto tries to stop her, which results in him being captured and forced to join the unit. However, this is part of his plan, and Mystique later stages an attempt against President Nixon's life so Magneto can break out.
When Mystique goes to Saigon to help the mutant unit escape, Toad takes the opportunity, and is later recruited to Magneto's brotherhood.
The timeline "fractures" in the end. The original timeline (which includes "X-Men Origins: Wolverine", "X2", "X-Men: The Last Stand" and "The Wolverine") remains the same, and the new timeline (which includes "First Class") is a clean slate, in which anything could happen. Old Xavier mentions he is able to feel the other timeline still.
Young Beast and Old Mystique share a brief moment in which he apologizes for not creating a better future, and she apologizes for not being able to change the past. Beast still harbors a crush on her and even attacks Magneto during the Kennedy assassination, under assumption he's trying to hurt her.
Wolverine's mind remains in his 1972 body. His future self is left in a comatose state.
The X-Men's hideout is an ancient tomb where Apocalypse lies dormant, though he awakens in the end. The comatose Wolverine might become his first Horseman in "X-Men: Apocalypse".