"We forgot to bring the movie. Okay if we just act it out for ya?"
I've got a feeling I'm going to be perceived as a hater for not being gaga, over-the-moon about X-Men: Days of Future Past, but, y'know - not every movie has to be the best thing ever. It's fun to see all these cast members together (though aside from Hugh Jackman and, very briefly, Patrick Stewart, none of the old interacts with the young), but is it too much to ask for a more complicated plot that would merit this all-star line-up coming together for an allegedly epic event?
In broad, spoiler-free strokes, the plot is simply this: Mystique (Jennifer Lawrence) attempts to do a particular thing, and then she attempts to do it again. There's a fair bit of window dressing, but that's essentially it, and it's spelled out in the first 15 minutes.
Were you hoping for inconsistencies in the previous films to be explained somehow by time-jumping? If so, tough luck; aside from explaining how Professor X can sometimes walk, that doesn't happen, but what does is that any continuity depicted subsequent to 1973 is more or less hand-waved away, as it's made clear right off the bat that Wolverine (Hugh Jackman), whose consciousness travels back to that year to prevent a Terminator-like future, will be changing the timestream by his very presence from the moment he gets there. From here on out, basically, the series can pick and choose what did or did not happen - it's akin to JJ Abrams' Star Trek timeline reset, but with more of the same actors returning.
"What do you mean, I'm not getting an action figure?"
The action begins in what is either the future or an alternate present - giant shape-shifting, mutant-power absorbing Sentinels are systematically killing off mutants and anyone with the potential to become one. A parental warning feels wise here: many characters, some loved and some less so, are killed both onscreen and off - that some of these deaths are later retroactively rewritten may not matter if your kid is easily upset by the initial shock, and those big black morphing voids are potentially quite frightening.
"I've got a hunger to play some games. Get it? Because I'm famous now."
Kitty Pryde (Ellen Page) turns out to not be just good at walking through walls, but also capable of sending peoples' minds back in time, so they can warn of surprise attacks before they happen. Most minds can't handle more than a day or so, but when Wolverine points out that his mind can heal from anything, they decide to send him all the way back to 1973, the year the Sentinels made their big debut. Now, you may be asking, if the Sentinels were built in the '70s and they've been steadily evolving ever since, where exactly were they in the other movies, aside from that one time in the Danger Room? Also, how did the world not know about mutants prior to Senator Kelly crusading against them in the '90s? If you are asking that question, and bothered by it, you may not enjoy the rest of the movie very much. [Rob will have a field day doing an FAQ on this, as would I, but preempting him on that one seems mean.] It really comes down to "Do I like this cast and crew enough to forgive the huge plot holes?" And since everyone reading this likes Patrick Stewart and Ian McKellen (and to a lesser extent Michael Fassbender and Jennifer Lawrence), most of you will probably say yes. Though a lot of you did not forgive them X-Men: The Last Stand, so who knows?
(Just so you know - I'm more okay with X-Men 3 than most people are. I'm exactly as un-okay with X-Men Origins: Wolverine as everyone else is. I generally like the rest.)
"Clap along, if you feel, like a mutant without a cape"
To achieve the goal of preventing Mystique from possibly doing the thing that will lead to the dark future, Wolverine must find a way to convince both young Professor X (James McAvoy) and young Magneto (Fassbender) to work with him. In the comics, such attempts usually begin with a big battle that ends in something of a draw, after which everyone agrees to be pals for the time being. Not so much here - given all they've seen, Charles and Erik are surprisingly easy to convince. They just still can't agree on how to get it done, with Magneto as usual being totally gung-ho for killing along the way.