How Baelish turned his beloved Catelyn against House Lannister
In the third episode of Season 1 ("Lord Snow"), Catelyn Stark secretly arrived to King’s Landing to investigate the attempted murder of her son, giving Petyr an excuse for a reunion. Littlefinger summoned Catelyn to one of his brothels, where Varys is also skulking around. There, Catelyn produced the dagger that an assassin (aka "catspaw assassin") used to try and murder Bran. Varys only recognizeed it as Valeryan Steel, but Littlefinger claimed that the dagger actually belonged to him… until he lost it to a bet to Tyrion Lannister. This is, we later learn, total bullshit.
Even with Catelyn within his grasp, Littlefinger didn't have the needed influence to get rid of Ned Stark, who was on his own mission in King's Landing. But he knew Jon Arryn was looking into the royal lineage and knows that will end up pissing off the Lannisters. Only now do we know that Cersei is not afraid to kill to protect her family, but three episodes into the series, Baelish wasn't sure his orchestrated conflict would reach a tipping point where he could take out Ned. Turning Catelyn against Tyrion eventually leads to Catelyn taking the dwarf hostage and inciting the War of the Five Kings.