Melody Pond is born, and subsequently kidnapped by Mme Kovarian, servant of the Silence, on the asteroid Demon's Run.
impossible astronaut (6.01) / day of the moon (6.02)
Melody's childhood is spent in an orphanage in American during the 1960s, where she is groomed to become an assassin. It is here that she first encounters the Doctor and is also shot at by her mother while in the spacesuit. Melody espaces the orphanage and somehow makes it to New York City where she does of starvation and exposure while homeless on the streets. She regenerates.
MELS ZUCKER
let's kill hitler (6.08)
While it's unclear how she made it from New York to Leadworth, Mels experiences a second childhood with her parents and kindles her obsession with the Doctor. A troubled child grows into a troubled adult, and eventually, Mels is able to meet the Doctor again by following Amy and Rory, and promptly hijacks the TARDIS. While her intention was to kill Hitler for the hell of it, she is the one who is accidentally shot. She regenerates.
Upon regenerating, River is finally able to accomplish what she had been groomed to do–she kills the Doctor. But then she learns about the person she will become, and how much she would come to love the Doctor, and so she decides to save his life at the cost of her remaining regenerations. Somewhere in there, she learns to fly the TARDIS, too.
let's kill hitler (6.08) / closing time (6.12)
Set on the right path, River is nevertheless left by the Doctor at a hospital in the 51st century to recover. He gives her the TARDIS blue diary by which they would chart their adventures. Eventually, River becomes a student of archeology at Luna University, but after receiving her doctorate, she is subsequently kidnapped by Mme Kovarian in order to kill the Doctor. Again.
the wedding of river song (6.13)
Forced to kill the Doctor, River finds a way out of it by tampering with the spacesuit. Her refusal very nearly destroys the universe, but then the Doctor makes her a promise in the form of a marriage, to be a part of her life. She kills the Teselecta!Doctor, and the universe is made right.
first night (6.00)
River is sentenced to 12,000 consecutive life sentences for killing the Doctor. She is imprisoned at Stormcage Containment Facility in the 52nd century, but does not always stay there. As promised, the Doctor arrives on her very first night in prison to take her out for an adventure: Calderon Beta to see the starriest night in the history of the universe.
a good man goes to war (6.07)
River appears at Demon's Run and reveals her identity as the daughter of Amy and Rory.
bad night / good night / first night (6.00)
River and the Doctor set out on a number of adventures during the first five years of her imprisonment, including some sort of hijinx where the Queen has been turned into a Goldfish; something to do with a haunted orchestra on the moon and somehow, Marilyn Monroe; and while she was evading a Sontaran Hen Night on Calderon Beta.
the pandorica opens (5.12) / the big bang (5.13)
At some point, River acquires a Vortex Manipulator from Dorium Maldovar and is involved with Amy and the Doctor's saving the Universe from total event collapse. In the process, she travels back to Ancient Rome, scares some Daleks are afraid of her and gets stuck in the TARDIS in time loop. When all is righted again, she tells the Doctor he will learn her identity soon.
impossible astronaut (6.01) / day of the moon (6.02)
River joins the Doctor and her parents in defeating the Silence in 1969, all the while being sneaky about not knowing that the little girl they are after is actually her. She gleefully gets to kill the Silence for her treatment as a child. At the end of their adventure, she kisses the Doctor for what she fears is the last time.
rain gods (7.00)
The Doctor is supposed to take River out for dinner, but instead, they almost become human sacrifices on the planet of the Rain Gods until their captors are struck by lightning.
the time of the angels (5.04) / flesh and stone (5.05) / the wedding of river song (6.13)
River, Amy, and the Doctor defeat the Weeping Angels at the crash of the Byzantium. Afterwards, River breaks out of prison again to pop by to visit mum and dad and lets it slip that the Doctor is really alive.
a good man goes to war (6.07)
Upon returning to prison after the Doctor took her to see Stevie Wonder perform on the Thames in 1814 for her birthday, River encounters Rory, who attempts to recruit her for the Battle of Demon's Run. Having already lived that moment, she has to tell him that she cannot be at the Battle until the very end.
the angels take manhattan (7.05) / last night (6.00)
Pardoned and released from prison when it was discovered that the victim of her murder never existed–a consequence of the Doctor erasing himself from databases throughout the Universe–River becomes a professor of archeology. The Doctor promises to take her to the long-promised Towers of Darillium, but changes his mind at the last minute.
the angels take manhattan (7.05)
Working as a private detective in 1938 New York, River investigates the invasion of the Weeping Angels. When she meets up with the Doctor and her parents, she is forced to witness their "deaths." The Doctor asks her to travel with him, which she says she will always do whenever he likes, but not all the time. Eventually, she begins the Melody Malone novel series which is later taken over by Amy.
the husbands of river song (9.13)
Back on her archeology beat, she travels with Ramone (a man she married, then subsequently wiped his memory of it) and Nardole. She marries King Hydroflax to gain access to an invaluable diamond in his head. In the process of recovering it, she encountering the Twelfth Doctor for the first time, and together, they defeat Hydroflax, crash a ship full of terrible people, and finally find themselves at the Singing Towers in Darillium. The Doctor gifts her a sonic screwdriver for Christmas, and they spend the 24-year-long night together. Happily.
silence in the library (4.08) / forest of the dead (4.09)
Professor Song arrives at the Library and meets Donna and the Tenth Doctor, whom she had summoned to the planet. They take on the Vashta Nerada and save everyone from the data core, but only when River switches places with the Doctor to use her own memory space to make the transfer. She sacrifices herself so that the Doctor can have all of their adventures to come. After she dies, the Doctor uses the fading data ghost on her sonic screwdriver to upload her consciousness into the Library's data core. Everybody lives. Sort of.
the name of the doctor (7.13)
While living her immortal life inside of the Library data core, she joins a conference call with Vastra, Jenny, Strax, and Clara about the Doctor. Her echo is able to travel with Clara and the Doctor to Trenzalore, where she finally gets her long awaited goodbye from the Doctor. It is suggested that her echo is able to visit the Doctor on occasion, but how? Spoilers.
* This timeline contains only the events that appeared as episodes of Doctor Who. River's canon timeline also includes adventures with earlier regenerations of the Doctor and their companions from "The Diary of River Song" audio series, Jack Harkness from the audio story "R&J," the audio anthology "The Tenth Doctor and River Song," as well as other bits of prose and comics that are described on her wiki.