I'm sure they gave an explanation for this plot point in Star Wars Episode VII, but I think I missed it.
How does Poe survive the crash on Jakku and get back to the Rebellion?
Seemingly the same way that Finn survived, when they ejected they landed too far apart and I am fairly certain that Poe said by the time he woke up it was already dark. So he was clearly out cold for quite some time, it's likely that his jacket was just left behind in the TIE fighter.
Common film trope to leave clothing behind in a crash only to have someone survive the crash / escape beforehand.
WGA script says merely:
What happened? I got thrown from the crash, woke up at night -- no you, no ship, nothing--
Foster Novelization says in Poe's words to Finn:
Finn studied him intently. “You look like you’re in one piece. I can hardly believe it. I thought you were dead: shot up in that TIE fighter we stole. I ejected. When I finally found the wreckage, I looked for you. Pulled your jacket out of your ship before it got swallowed by the sand. What happened to you?”
“I wasn’t dead, just momentarily out of it,” the pilot explained. “Came around long enough to see that you had got out. Pulled out of the dive just long enough to set down—hard. Impact threw me clear. Woke up at night; no you, no ship, no nothing. Went looking—in the wrong direction. Got picked up by some itinerant trader.” He grinned. “Tell you all about it sometime.” A plaintive beep caused him to turn and look down. “Beebee-Ate says that you saved him.”
and earlier, elaborates from the narrator:
His name. That was his name. Poe Dameron, and he was a pilot in the Resistance. But if he was a Resistance pilot, where was his flight jacket? Probably still pinned in the TIE fighter he had only just managed to set down in one piece. He remembered the crash now.
Remembered recovering consciousness just in time to set down more or less intact, trying to get out of the cockpit before something blew, his jacket caught and holding him back, struggling out of it and then tumbling clear onto the sand—all of it recalled through the haze of his concussion.
That is detailed earlier in novelization. Too much text to get the quotes, but in short, he met a salvager named Naka in the desert.
“I just escaped from the First Order by stealing one of their advanced TIE fighters, used it to shoot up one of their Star Destroyers, and crash-landed somewhere near here.”
Naka stared at the human for a long moment. Then his wide eyes squinted, his scaly cheeks caught the sun as they bunched up, and he burst out laughing. One five-fingered hand wiped at the tears that trickled from the corners of his eyes.
“I’ll wet my zinz if you aren’t the most barefaced liar I’ve encountered in twenty years of scavenging on this sandbox!” He extended one lightly clothed arm. “Come with me, my friend. The Blarina do say that much good accrues to anyone who helps the mad. Liar or madman, whichever you may be, it amuses me to lend you assistance.” Lowering his eyeshades, he turned his gaze skyward. “The spirits have placed you here to alleviate my boredom. Come.”
Then he agrees to take Poe to another Blarina in town, to help him get off-planet.
Naka’s grin returned, his sharp teeth glistening in the bright sunlight. “We’re also famously accomplished liars.” He glanced once more at his passenger. “I’ll take you as far as Blowback Town. There’s a Blarina merchant there named Ohn Gos who is afflicted with the sorry habit of listening sympathetically. I’ll introduce you. After that, you’re on your own.”
“Oh joy, oh pleasurable delight!” A hand reached over to clap Poe on the shoulder. “Saved by a madman!” The Blarina pointed. “Our destination lies that way. I find myself suddenly amenable to letting you drive. Are you really with the Resistance?”
“Yes.” Compared to a stolen TIE fighter, the speeder was easy to operate.
“Then you truly are crazy.”
Poe glanced over at him. “We of the Resistance prefer the term ‘courageous.’ ” “I see little difference.” Leaning back in the passenger seat, Naka Iit picked at an incisor with one claw-tipped finger. “I owe you, my madman friend. Beyond just picking you out of the desert, I owe you most thankfully. I will intercede with Ohn Gos. One way or another, we will get you off Jakku!”
“I’m grateful,” a relieved Poe told him simply.
“Grateful! What matters the gratitude of a madman?” Naka replied.
But he smiled as he hissed it.