Basically, when Kara and Kal left Krypton, Kara's pod hadn't gotten quite far enough away from the planet when it decided to do an impression of Alderaan. The shockwave knocked her pod off course and into the Phantom Zone, a place where time doesn't matter and, seemingly, people go into a kind of stasis (Kara only remembers the pod going off course before crashing on Earth... this jives with the idea that she didn't age. My thought is that because time doesn't exist in The Phantom Zone, biological processes are halted and memories aren't stored for when you leave, meaning that you are the exact same person upon leaving as you are upon entering). She remained there for 24 years until, for some unknown reason (I will detail out my theory on this below), Kara's pod was released from the Phantom Zone and crashed on Earth. When she crashed, an already adult Superman (presumably 24 years old and already fully realized as Superman) came to her rescue, broke her out of the pod, and took her to live with the Danvers (the scientists who helped Superman understand his powers) and their daughter Alex. Because Kal had no need of her to protect him growing up and because he was fully in the role of Superman, Kara decided to live a normal, human life. She always had her powers, but didn't exercise them other than to keep them in check (like not breaking someone's spine when giving them a hug... she hasn't flown in years). Now, it's twelve years later, making Kara about 25 (given her age of 13 when she left Krypton) and Superman around 36.
Given that Arrow, Flash, and the upcoming Legends of Tomorrow and Supergirl are supposed to be in a shared universe, you're wondering why we haven't heard anything about Superman's exploits on The Flash or Arrow.
Well, I have a nifty explanation that makes sense (to me anyway, but I don't vouch for my sanity here). The season finale of The Flash has Barry running into a wormhole above Central City in an attempt to destabilize it and keep the planet from getting swallowed. Now, this wormhole that formed over Central City, sucking things in, bears a remarkable resemblance to the wormhole to the Phantom Zone in the Supergirl pilot, which we know from the pilot allowed Kara's pod and Fort Ras (the Phantom Zone prison) to leave The Phantom Zone.
We know that, supposedly, Season 2 of The Flash will feature Earth One and Earth Two.
We also know that while the four shows all supposedly exist in the same continuity, CBS wants to keep Supergirl to themselves for a while before any crossovers happen.
What if Supergirl takes place in one of those two universes while The Flash, Arrow, and LoT take place in another? What if the temporal paradox created by the death of Eddie and the erasure of Reverse Flash opened up a portal between the two universes through The Phantom Zone?
If you think of a wormhole using conventional thought processes, it has an entry point and must have an exit point. Whatever goes in HAS to go somewhere, which would displace whatever is already there, causing it to exit the other side.
Given that time is meaningless in The Phantom Zone, it would mean that all time simultaneously exists and doesn't exist in The Phantom Zone. Basically, if you go in, you will arrive at the same time as everyone else. If you leave, you will leave when everyone else does. It doesn't matter if you are there 30 seconds or 30 billion years.
Now, according to the pilot, Fort Ras was released from the Phantom Zone only because they latched on to Kara's pod somehow and followed her out, which would explain why they emerged at the same time.