SPOILERS AHEAD! If you haven't finished watching Stranger Things, what are you waiting for? Go do that instead!
We all remember that moment, Eleven sacrificing herself for her friends. Disintegrating herself along with the monster as her powers overwhelmed her. Then, in the end we're given a tiny, shining thread of hope as Hopper leaves some Eggo's in a small forest cache.
So what's going on here? We saw Eleven die! Except, if you look closely, we didn't.
At the moment just before the cloud vanishes Eleven is completely obscured by the ashen remains of the monster's body. This is the critical moment where she takes an opportunity to disappear, knowing the boys aren't watching and no one else is around.
But how? Her powers are extensive, but if we assume all of her powers were used at some point during the series we must conclude she can not teleport, nor turn invisible. Further supporting those limitations is the fact that she merely ran from Benny after being spotted, ending up captured rather than becoming invisible or teleporting away.
We can similarly reason that she is unable to travel to the Upside Down using her abilities. There are many instances where she could have saved Will, or provided passage for the others if she could do so. Instead they had to rely on drawing the monster to them, or using the portal at Hawkins Lab.
The monster, however, can travel between worlds at will. Furthermore, the monster's secretions appear to be capable of creating portals between the Upside Down and the normal universe. Secretions that Eleven was manipulating at nearly an atomic level!
It is clear that Elle was able to use the monster's disintegrating body to build a short-lived portal to the Upside Down. From here she must have run back to the only other portal she knew of at Hawkins Laboratory to make a return to the real world. Certainly the lab holds a lot of terror for her, however at this point most of the personnel are dead either by her own mind or the monster's hands. Given that we've also seen she can manipulate radios, it's likely that she can manipulate cameras as well to prevent any recordings of her escaping the lab.
From there she could have find shelter in Castle Byers, simply hiding whenever Will comes by, and she must have contacted the Sheriff for food.
The only question left is why she would run away from her friends. This is obvious, really. Her mere existence poses a danger to her friends. If even one person outside of that town discovers this story, and tries to use her powers, her friends would be harmed.