When River Song died of starvation in New York, she regenerated into a toddler. She was soon picked up by the Silence priests who took her off world because the space suit had failed to contain her. Unfortunately, due to freak circumstances, they accidentally were sucked through a hole in the time vortex and, much like the Doctor and Rose, found themselves in an alternate universe...one in which the only species in all of time and space were humans. In the current setting, the Earth's been used up so the humans have spread across the galaxy Terra-forming new earths. The central planets, those which had the majority of the money, formed The Alliance. It was a ship from one of these planets that found the Silence's vessel and newly regenerated baby River on board. They found and were able to decipher writing with her name on it, (the Silence, after all did have a presence in multiple time lines and new about Melody Pond's future alias), but the priests had ceased to exist because, in the rules of this dimension there were no other alien life forms.
River, being mostly human, genetically, managed to survive the transition. Though she was technically a human and, to all who saw her, a young human, little River retained her memories and her great Time-Lord like intelligence. The Alliance-run vessel arranged for her adoption to a rich family, the Tams. River Tam finally had the supportive and wonderful home life that she had been denied thanks to Madam Kovarian in her new father and mother, and especially her older brother Simon. She flourished in this setting and her natural brilliance did as well—quickly getting her noticed by the Alliance who were on the lookout for special children. As a teenager she was offered a special chance to go to an advanced school for geniuses—she was eager to learn and begged her family to let her have this opportunity. She didn't know that it was a trap.
Young River was being experimented on in this academy. The scientists had no idea why their methods, which had met with limited success in previous patients, were so successful with young River. They did not realize that the type of training and torture they were performing on the girl were the same things the Silence had done to her in a previous regeneration. The Alliance scientists assumed her success was due to her talented and gifted mind, and, of course, their own advanced methods. They called her a 'prodigy' and patted themselves on the back for creating the perfect weapon...the perfect psychopath.
River Tam, on top of the physical and mental torture she was going through, was now also having flashbacks to previous lives and experiences—memories that she had tried to block while living with her parents and her brother. To keep from losing her mind completely, she called out for help to her family, knowing her wonderful big brother Simon would save her. While she waited for him to come and get her out, the torture continued and cracks started to form in her sanity and reason. She was more and more open to the thoughts of the people around her, and those thoughts and memories, combined with the past memories of a girl involving a carnivorous space suit and endless brutal training—memories that faded into what was happening to her at present, were taking a toll on the young girl. It wasn't long before the doctors began calling her unstable and started sedating her more and more. The torture continued and River's mind became more and more filled until she almost couldn't bear it.
When Simon finally managed to rescue her, it was a broken and shattered mind that was in the body of River Tam. Too many voices screaming at her, some from worlds in this universe, some in another—it was more than any child could take. Simon, a brilliant doctor now, devoted himself to caring for his sister and keeping her out of the hands of the Alliance, who desperately wanted their toy back. To that end, Simon managed to secure room and board on a pirate vessel, Firefly class, named Serenity. It wasn't long before Captain Mal Reynolds and his crew more or less adopted the Tam siblings and they were as safe as could be expected. River's mind was no better, but the torture had ceased and her brother did his absolute best to care for her.
They had many adventures while on the crew of Serenity...the stories of which can be looked up elsewhere, but River's mind was never fully restored to what Simon remembered as his little sister. Unfortunately, the dam had cracked and the memories of her other life, of being trained and conditioned for that one terrible purpose of killing the Doctor kept spilling through. She had learned other secrets from the Alliance, and, eventually, she was able to share them to help the crew that had adopted her right a terrible wrong the Alliance had committed. In the process, during a battle, River allowed herself to fully access the training she had received in both this universe and the last, fulfilling a purpose that had been a part of her life from before Simon was even born. It healed her in ways that her genius big brother could not understand.
There were, in fact, many things that Simon didn't understand about his little sister after that terrible battle. Though they had won the day, it was at great cost—but a cost that little River did not seem to feel. Simon didn't know how to respond to this laughing, joking, witty River who so resembled the sister he remembered from his childhood when she could, and would, carry a gun around like Jayne and was just as at ease with the mercenary as she was with her old friend Kaylee, whom Simon was now romantically involved with. In many ways, River was much better than she had been since he first rescued her—but in many more, it was almost like she was a stranger to him now.
River noticed and subtly encouraged the growing distance between her and Simon. While she loved her brother and would always be grateful for his affection, support, and rescue, it was time she got back to her real life, her real purpose, which lay in an entirely other universe. River used the opinion the others had of her as slightly crazy but innocent and naïve to pick their brains about the best way to get back to her home dimension. As a child of the TARDIS, she knew she could work out how to get back if she could just work out the best place to start.
While Serenity was on a job, River slipped away unobtrusively to remotely hack into the Alliance network. Between what she had learned from the minds she was exposed to while at the academy, her own remembered brilliance, and her time near the ridiculous man called Mr. Universe, she was sure that if anyone know where a temporal and spatial weak point in the universe would be, it would be the busy-body Alliance.
She was right. Using the information she had found she started making plans. It wasn't long before she realized that she'd be able to control where and when the ship landed...but she probably wouldn't survive the trip. The vessels in this universe just didn't have temporal shielding—she might be able to break through the weak point, but the passage would more than likely kill her. The knowledge didn't slow River down for a moment—she was always willing to bet her life.
It took some doing...knowing Simon the way she did, plus the determination and almost fanatic loyalty inspired and modeled by Mal, River knew that if she wasn't careful about how she left, the entire remaining crew of Serenity would likely try to follow her into the void. They, unlike she, did not have the ability to regenerate and would have absolutely no chance of survival if they attempted to make the journey with or after her.
So River distanced herself from the crew even more. Years have passed at this point and River has proven herself a useful and necessary member of the crew—her abilities as a soldier, her intelligence, and her sensitive abilities that were honed by the Alliance doctors meant that she had proven so vital to their lifestyle that she was almost never questioned when she made a decision, even by Mal. They all trusted her, but none of them knew her. Simon didn't like the fact that his sister didn't seem to need him much anymore, but in some ways he was secretly relieved to have the pressure of caring for her to the exclusion of any other relationship removed from his shoulders. He and Kaylee were due to get married soon and the Alliance had taken a major hit when the secrets on Miranda had been revealed so the price on his and River's head had all but disappeared from the minds of bounty hunters. Life was good.
River talked to Mal about a possible job in the same region where the weak spot existed just out of the time stream that this universe ran in. Once she manipulated them into getting into the general area, she tipped their hand to the crime syndicate they were attempting to rob. In the ensuing chaos and firefight, she put the plan she had been developing for more than 22 months into action. Cloning may have been outlawed on the central planets, but out here in the black, on the outer rim, it was possible to find pretty much anything (especially if you had a smuggler's reputation and contacts). River dragged out the clone she had managed to sneak on board, shot two bullets into the vegetable's brain pan execution style (no reason to leave her brother thinking she had suffered), left the body and went to the ship she had designed and arranged to have waiting for her on this out of the way border planet.
The plan, having gone off without a hitch, ended with River flying alone through the temporal-spatial hole, unknowingly cracking a small rift in the fabric of reality that would later be magnified a thousand times when the TARDIS exploded thanks to the Silence. When her ship made it to the other side, it was floating above the Earth, dead in space, with basic back up life support the only functioning system—and that one failing quickly.
River was in bad shape. The travel through the vortex in an only partially shielded vessel had not only poisoned her cellular structure (something she had predicted) but it had tampered with her mind. The psychic powers she had developed in that other reality were slipping away...even her identity as River was slipping away and, in a panic, barely conscious, she seized onto the thought that had guided her when she chose the time and location where she would come through the rift—she was Melody, the daughter of Amelia Pond and Rory Williams. She held onto that thought so desperately that it was the only thing in her mind when the regeneration process started.
The damage her ship had sustained was soon too much to withstand Earth's gravity. There was just enough shielding left that it survived the descent into Earth's atmosphere, but the resulting crash into the waters off of the UK was something, had she not been in the middle of regenerating, even she wouldn't have been able to survive. When she managed to get ashore, it was after she had fully formed into a child again—a dark-complexioned girl of about age five.
She still had that one thought in her head: She was Melody, the daughter of Amelia Pond and Rory Williams. The young Melody knew she wanted to find them. It wasn't long before her other memories started to resurface, the most recent first—she knew she wanted to get to Leadworth, knew her parents were there. When she was found wandering the beaches, she explained that she was Melody Smith, from Leadworth. They helped her get to the area, but when she was unable to produce her parents or a home address, she was entered into the system and adopted there in town. It wasn't long before she found the people she was looking for—young Amelia who constantly talked about her Raggedy Doctor (a man Melody was remembering more about each and every day; a man she knew she was destined to kill in the future) and hopeless, bumbling Rory who was already in love with an oblivious Amelia.
She made herself their friend, waiting for the time when the Doctor would return for Amy Pond—she had remembered her purpose and training. She knew he would come some day and that that the resulting adventures would lead to her own birth. Melody even knew how to work hallucinogenic and poison lipsticks, though she had to wait a few years before she could make use of it since she had regenerated into such a young thing. The only thing she could not remember was her time in that alternate reality—River Tam, her family, that past, that whole universe and it's adventures, were left far behind and were wiped from her memory forever.