"Bucky is the equivalent age of Steve Rogers and is physically taller than him prior to Rogers’ Super-Soldier enhancements. After Captain America (Rogers) saves him from HYDRA, Bucky joins his handpicked unit clothed in a blue jacket that vaguely suggests his original incarnation’s costume. In the comic book tie-in to the film, it is revealed that the movie’s version of Bucky met Steve when they both were children, and then they both became friends after the young Barnes saved Rogers from bullies. He was recruited by Rogers as part of his special team. During one of his incursions onboard a train, which turned out to be an ambush by Arnim Zola, he fell to his apparent death when a weapons blast knocked him out of the train and over a cliff into a distant frozen river." - taken from Wikipedia. This is where comic canon ends and ‘Bucky’s writer makes shit up’ begins. Buckle up, kiddos.
At some point after his fall, due to Zola’s experiments, he was found alive but unconscious. He was taken in by the Russian’s and before he could wake up, he was put on ice. They knew they wanted to do something with him but they weren’t sure what. He was special - because of what Zola had done, and they didn’t want to throw away an potential. So, for about thirty years - 1980ish? - Bucky was on ice. Then, they woke him up, gave him his arm and started the indoctrination.
Attempting to replicate healing and cell regeneration like Wolverine’s and the quick healing of Cap, they put him through more tests and eventually he came to the point where he no longer ages at a measurable rate. He can be hurt, but he is biologically immortal, as in diseases will not kill him, nor will growing old but any external force can injure him if it is strong enough, just like Cap. He was trained to be a brutal killing machine as we know and he helped train Natasha. Their relationship with short lived. After the attack by Loki, and the Avengers coming to light as a real threat against evil, Winter Solider was sent to kill Cap.
Sometime after arriving in NYC to scout and do recon to prepare, slivers of memories began to work their way through the brainwashing. If the brainwashing had put up a physical wall in Bucky’s head, this was the first crack. Along with the regeneration experiments, the doctors had far from given up on the SS serum and while it didn’t do to Bucky what it did to Steve, it did make him smarter and stronger. His brain resisted the indoctrination from day one, and being in NYC unsupervised meant his brain was exposed to thing that could cause a memory to trigger. One memory, just one memory that was just strong enough would be all it it took to break through everything else that remained between the truth about Bucky and what his captors had told him.
This trigger came in the form of recon while gathering intelligence on his target and the Avengers. He simply came across a Natasha’s SHIELD file while hacking, and his own name was in it as well as information on a man named Bucky Barnes and his connection to Steve Rogers. He decided to physically follow the team for a while, most around NYC and mostly Steve. He saw the team in action during a close to home mission and seeing Steve as Captain America basically destroyed him and I mean hardcore PTSD, not sure who he is or what is real. He did not actually have true hallucinations but prior to Natasha tracking him down after a brief run in on the streets of NYC, he assumed everyone who he saw or spoke to from his past was in his head. He still isn’t sure what the hell is happening but he has a safe place now, in custody of SHIELD.
For the most part, it isn’t for his safety, but for the safety of everyone else. He is more volatile than the fucking Hulk at this point. On the bright side, during his recon he gathered some intel on the colliding universes so while it’s not helping him establish himself as sane, he’s aware of it. He has managed a deal with SHIELD and Fury that works for him at the moment. He is not an Agent of SHIELD but he works along side them, involved in the missions that Fury deems important.