Baelish will get found out this season and meet a grisly end. I'm going to guess at a timeline.
First couple of episodes: As we've seen in the trailer, Jon and Baelish have a conversation in the crypt - probably about Jon's heritage or that he's not a "proper king" - remember that it was Baelish who told Sansa the story about Rhaegar and Lyanna in season 5. The conversation leads to Jon becoming a bit wound up and pushing Baelish up against the wall, mirroring Ned's first meeting with him in season one outside the King's Landing brothel. Littlefinger will use this chat as an opportunity to get the measure of Jon, to see how easily he can be wound up, and will begin to plant the idea in Sansa's head that she's a more worthy ruler because her temper is cooler and she's a better strategist - "Jon can't be trusted, that's why you didn't tell him about the Knights of the Vale" he'll say to her. Sansa will begin to doubt Jon, and if she's got even the slightest inkling that he's a Targaryen there could be more trouble in the works.
Mid-season: Jon has left Winterfell to go north beyond the Wall, leaving Sansa in charge. Baelish takes this opportunity to show Sansa she can manage the politics of the North by herself, that she could easily step in and do the job if Jon were to die beyond the Wall. Arya and Bran have both arrived back at Winterfell, but the reunion doesn't last long as Baelish immediately sets about causing a rift between the Stark children, playing on the fact that Arya and Sansa never got on in the first place. Cracks begin to appear in the relationship between the Stark children.
Final two/three episodes: Something happens to make Sansa reconsider things. Maybe Brienne says a few wise words. This, I imagine, is where the "The lone wolf dies but the pack survives" speech will come into it, that Sansa, Jon, Arya and Bran need to stick together when the full force of winter arrives. Maybe the show will make it really convenient and wrap it up easily, with Bran looking into the past and seeing that Baelish betrayed Ned, murdered Jon Arryn and that his feelings for Sansa are a mixture of necrophiliac lust for Catelyn and his own desire to take the Iron Throne. He's betrayed a Stark to get what he wants before, and he'll betray a Stark to get what he wants again. With everything out in the wash, Sansa sentences Baelish to death and Arya carries out the deed with his own dagger. Everyone goes home happy.