The Daily SuperHero has put my own theories online about this and while the easy answer would be to say that Magneto helps Logan reacquire his metal claws, I've resisted that explanation because it's just too simple. And quite honestly kind of lame. But it seems like a simple answer might be the actual answer.
Potentially taking the easy way out of explaining this mystery, director Bryan Singer spoke with Empire Magazine (via Screen Rant) about the adamantium claws.
"Director Bryan Singer explains that Magneto’s ability to manipulate metal might have something to do with it. The Master Of Magnetism could, perhaps, 'reconstitute the adamantium claws… [Wolverine] has a different relationship with Magneto, and perhaps Magneto could forge them.'"
So there you have it. I was wrong (maybe) and it seems like the easiest explanation could be the correct one.
X-Men Days of Future Past is out in theaters on May 23, 2014.