Their overall plan was to have the Doctor killed. According to a prophecy, "On the Fields of Trenzalore, at the fall of the Eleventh, when no creature can speak falsely or fail to answer, the question that must never be answered will be asked." The Silence wanted to prevent that from happening; they determined that the Doctor was involved. So, they were going to kill him by raising the perfect weapon: his companion's child into a psycopath. They kidnapped Melody Pond and tried to get her to kill the Doctor several times; every time failed. The Silence then made one last failsafe: They made a fixed point in time. So, the Doctor had to be killed, otherwise the Universe would die. That's what the Silent's plan was in "Day of the Moon".