In the books we have so far, here is the plan he says he has (so keep in mind this may not be his entire plan or even his real one) and what we can mostly infer.
After he kills Lysa, Robert/Robin's epilepsy becomes more and more pronounced due to the stress of his mother's death. Littlefinger tells the Eyrie's maester to begin treating him with a drug called sweetsleep. A few grains of this will calm a fit, a pinch will put someone to sleep, and three pinches are fatal. The maester disapproves of this treatment, stating that sweetsleep doesn't leave the body with the implication that prolonged use can be fatal even with small doses. So while Littlefinger doesn't outright say it, he's most likely planning to kill Robert/Robin.
He tells Sansa that he plans to wed her to Harrold Hardyng, the cousin of Robert/Robin and his current heir. So if Sansa marries Harrold and Robert/Robin dies, she will be the Lady of the Vale. Keep in mind that the Vale is the only one of the seven kingdoms to stay out of the war; their armies and resources aren't depleted in the slightest. So you can kind of guess his plan from here: use the armies of the Vale to take back Winterfell. Once he reveals Sansa's identity, what remains of the North and the Riverland armies will flock to his banner. So he has the armies of three kingdoms to take King's Landing and install Sansa as queen.
And somewhere in that, he's going to bang and/or marry her to be King.
Well it certainly sounds better than what we've gotten in the show which is just indeterminate scheming. ---