Littlefinger worked on the plots to kill Jon Arryn and kill Bran Stark because he was secretly working with/for the Lannisters in season 1 and in the year before season 1.
Cersei wanted Jon Arryn dead because she feared he would learn that her children were incest bastards of her brother, and not true heirs to the Iron Throne.
Cersei wanted Bran Stark dead because the boy saw Cersei committing incest with her brother, Jaime. If Bran mentioned it after recovering from the fall, King Robert Baratheon would have her killed for adultery. Robert would also kill Jaime and the children.
Cersei probably appealed to Littlefinger to help with the plots against Bran Stark and Jon Arryn.
Littlefinger likely went along with the plot to kill Jon Arryn because with Jon Arryn dead, Littlefinger could move forward on his plan to marry Lysa Arryn and become Lord Protector of the Vale.
By helping in the plot to kill Bran, he can implement the assassination plot in way that makes it look as if Tyrion Lannister was involved. That would sow distrust between the Starks and Lannisters, which would create chaos in the 7 kingdoms and allow him to advance another rung up his ladder.
We see a direct confirmation that Littlefinger worked for the Lannisters in season 1 when he betrayed Ned Stark. Ned Stark had learned Cersei's secret, and she could not allow Ned Stark to live. So she probably asked Littlefinger to betray him too.
It is only in a later season do we see Littlefinger working against the Lannisters. His early work for the Lannisters was just one rung on the ladder to his own personal success.