How did Sherlock survive the fall?

He jumped into the truck which was in front of the pavement and drove off as soon as he pushed a body out wearing his clothes or he landed in the truck and then rolled from the truck to the pavement.

Remember how he told Watson exactly where to stand? (to make sure he could only see from the correct angle)

Watson was delayed by a bicycle hitting him as he ran over. (to give Holmes and co some extra time)

Watson was pushed back by bystanders telling him not to look? (so he would not spot any inconsistencies but would see enough)

Suddenly medics appeared and rushed off with the body? (to prevent Watson, or anyone else, looking too closely)

Holmes remarking to Molly that he needed her?
(either for a spare corpse or to falsely pronounce him dead)

This fits well with the books where Holmes often keeps Watson in the dark, especially as Watson is a very poor liar.

I theorize that Sherlock JUST DID JUMP (1). He did, however, have a means of breaking the fall presumably by the exact same means that helped one of the CIA operatives survive in 'A Scandal in Belgravia'. If you recall, Sherlock was asked on the phone by Lestrade:

LESTRADE: And exactly how many times did he fall out the window?

SHERLOCK: It’s all a bit of a blur, Detective Inspector. I lost count.

And from Mrs. Hudson when we hear Neilson fall from the room:

MRS HUDSON: Ooh. That was right on my bins.

Since we know that the CIA operative (Neilson) was able to survive multiple falls and he was still in standing-condition, I propose that Sherlock did the exact same thing: foreseeing that he was going to have to jump (2) even from a height much higher than what Neilson had to do, he did so but was more severely injured. The fact that Sherlock also was sitting (rather than standing with a cane) in the final reveal supports this idea.

For me, it's certainly plausible that Sherlock gave the biker some of that hallucinogen to get Watson to believe Sherlock was dead. However, one thing I don't necessarily understand is why he would have required Watson to be alone in that 'poisoning'...in that if he also got the pedestrians nearby affected, they would further corroborate the idea he fell and died (which is what their suspicions were, likely, anyway). Of course, it does make sense that he kept Watson so far away (because then he might have identified the means Sherlock had to break his fall).

Molly assuredly was part of the plan (3) (his means to get past the coroners and proclaimed dead) and because of how Irene got proclaimed dead as well, I have every reason to believe Mycroft was in on it (4) , too (explaining his disinterest when he reads about it).

Lastly, I also believe that this would have had to have been convincing EVEN IF Moriarty did not shoot himself, which makes 'jumping onto a truck' less viable...not to mention it seemed clear to me his downward falling trajectory couldn't possibly have landed on the street, anyway.

On a TANGENT, one of the more popular theories I've read was that it was a double and that Hallucinogen + Facemask is how he faked his jump (akin to how the kidnapped children were afraid of Sherlock). But I refute the facemask idea for reasons of inelegance, as well...not to mention that it seems fairly clear how those children were scared. Richard Brook was a real persona created by Moriarty (as 'the Reader') in which he used the television show to tell stories of Hansel and Gretel and (though not shown on the series), with a very good likeness of Sherlock (5) over television, condition the two orphans (and probably lots more children!) to be afraid of him when they finally saw him.

Edit: added corroborating evidence from S3E1 by the numbers:

1. (Sherlock spreads his arms to either side and falls forward, plummeting towards the ground. Inside the building, Molly gasps as he falls past her window. We see from John’s point of view that the last thirty feet or so of the fall are blocked from his view by the station. Unseen by him, Sherlock is plunging towards the airbag, twisting as he goes.)

   SHERLOCK (voiceover): I needed to hit the airbag – which I did.

2. SHERLOCK (voiceover): There were thirteen likely scenarios once we were up on that roof. Each of them were rigorously worked out and given a code name. It wasn’t just my reputation that Moriarty needed to bury – I had to die.

3. SHERLOCK: Molly found the body, faked the records, and I provided the other coat. I’ve got lots of coats.

4. SHERLOCK: Mycroft’s men intervened before he could take the shot. He was invited to reconsider.

5. SHERLOCK: You assumed she reacted like that because I was her kidnapper. But I deduced Moriarty must have found someone who looked very like me to plant suspicion, and that that man – whoever he was – had to be got out of the way as soon as his usefulness ended. That meant there was a corpse in a morgue somewhere that looked just like me.

There are several things that you had to notice to put this together:

1. Sherlock asks for Molly's help. With what? I'm gonna get there in a sec.
2. Sherlock talked to the homeless network earlier in the episode for unknown reasons.
3. Sherlock tells Watson exactly where to stand
4. There is a truck full of garbage bags near the place where Sherlock lands. Before the truck arrive, there is an out of service bus parked in that spot to save it. You can tell it's out of service because it's parked there for the duration of Sherlock's conversation with Moriarty, and there's even an old man banging on the door with a cane to no avail when Sherlock first stands on the ledge.
5. Earlier in the episode, Sherlock is bouncing a ball in the hospital.
6. Sherlock calls the reporter, Riley I think her name was...

Sherlock is on the roof of a hospital, meaning that there is no need for an ambulance. He tells Watson exactly where to stand, and he tells Watson to keep his eyes on him the whole time so that Watson will not notice anything going on at the foot of the building. Sherlock jumps off the building into the truck. He could then get out of the truck and lay on the sidewalk.

The bicyclist that hits Watson is part of the homeless network and hits him to disorient him, so he can't get to the body quickly. Also, the crowd of people that surround Sherlock's body are also homeless network people, because they make it impossible for Watson to see Sherlock's body right away.

Watson goes to Sherlock's body, and checks the pulse. He doesn't feel a pulse, but there is an explanation for this. When the ball Sherlock was bouncing is squeezed between your arm and your body, it makes the feeling of a pulse disappear from your wrist. Sherlock is rushed into the hospital, which does not let Watson accompany Sherlock, and Molly declares Sherlock dead. Watson has to believe this because there is a funeral (for closure), and there is no other explanation.

My favourite theory is akin to the answer given above, but with the extra that when the cycle courier bumped into Watson he exposed him to the chemical from the previous episode that induces hallucinations of that person's worst fear.

It's been a while since I've seen the episode but I do remember that Watson got a clear look at the body on the ground, rolled it over and saw Holmes face. My theory is that by this time the body had already been swapped out, and it was the effects of the hallucinogen that made Watson see the body as Holmes when in fact it was A.N.Other.

In January 2014, Steven Moffat provided some insight in an interview on how Sherlock faked his death:

As we keep saying to people, I do think there was -- I can now say this -- a measure of nonsense going on. He's falling off a building. He has one objective -- that is, not to hit the sidewalk. That's it. That's the only thing he can do. Didn't anybody notice that there's a whole building between John and the point of impact? So obviously something got in the way. That's it. It wasn't going to be anything else. The TARDIS wasn't going to fly in. That wasn't going to happen."

Since Moffat's explanation best corresponds with the final explanation provided in the episode itself, I think the official answer is--disappointingly--that Sherlock jumped on the airbag shown in @howlers answer.

His lackluster answer fails, though, to address a number of different plot holes. For one, what happened with the assassins set to kill Lestrade and Mrs. Hudson?

ANDERSON: And what about the sniper aiming at John?

SHERLOCK: Mycroft’s men intervened before he could take the shot. He was invited to reconsider.

But according to The Reichenbach Fall, on the roof:

JIM: Okay, let me give you a little extra incentive.

JIM: Your friends will die if you don’t.

SHERLOCK: John.

JIM: Not just John. (In a whisper) Everyone.

SHERLOCK: Mrs Hudson.

JIM (in a whisper, with a delighted smile): Everyone.

SHERLOCK: Lestrade.

JIM: Three bullets; three gunmen; three victims. There’s no stopping them now.

JIM: Unless my people see you jump.

We have little reason to believe that Sherlock could anticipate three assassins, as he likely was hearing about these assassins for the first time on the roof. But by sheer luck, Mycroft and his men were able to locate one sniper and successfully coerce him to call off the other snipers. It turns out there was only a single hired gun watching Sherlock rather than the multiple people ("my people") he claimed needed to witness Sherlock jump. Seeing how Moriarty did not establish a pattern of lying (nor did he need to), this seems less realistic.

Further, Sherlock did not anticipate Moriarty's suicide. He spoke the following words to John, which seems unlikely a line to lie about:

SHERLOCK (voiceover): But the one thing I didn’t anticipate was just how far Moriarty was prepared to go. I suppose that was obvious, given our first meeting at the swimming pool – his death wish.

But he also says he planned out for likely scenarios:

SHERLOCK (voiceover): There were thirteen likely scenarios once we were up on that roof. Each of them were rigorously worked out and given a code name. It wasn’t just my reputation that Moriarty needed to bury – I had to die.

Put another way, Sherlock admits he didn't anticipate Moriarty dying, but he had thirteen scenarios planned for; one of which involved an empty street, an enormous blue airbag, and a taxi driver letting Watson out exactly at the right place. With Moriarty potentially alive, could this have been a plausible idea?

I think Moffat got outmaneuvered by the most fanatic viewers, and conceded early on before filming there were more fitting theories out there, but they were unable/unwilling to pull it off in the timeslot and writing:

As to the theories that were presented online, Moffat says he is aware of them, but that for the most part, the audiences explanations are far more complex than what the show ultimately needed. (emphasis mine)

"Needed" being the operative word, as there are many people perfectly satisfied with this explanation and a much smaller minority who are severely outraged at its incompleteness or implausibility.

Going deeper into the meta, I think Moffat knew he was denying us sufficient closure. As we as viewers find holes in the story and receive no answers, Andersen finds holes in the story and Sherlock abruptly disappears, leaving Andersen to completely break down. Of course, Sherlock fanatics are Andersen in this metaphor. /fanaticism

He used an inflatable crashmat hidden by a low building, and a cyclist who deliberately knocked John to the ground, buying time for Molly and members of Sherlock's "homeless network" to bloody up his “dead” body and take away the crashmat , The squash ball under the arm to mask Sherlock's pulse – a technique used on stage by Gatiss's friend Derren Brown was used when watson checked for a pulse

I don't think anyone can answer this question for sure until the next episode comes out but my observations.

Sherlock asked Molly for help but the audience didn't find out what for.

Moriarty actually told Sherlock he was going to fall!

Sherlock chose the location, not Moriarty

Could the cyclist who hit John be part of the homeless network?

The bicyclist is Holmes. He calls Watson from his cell so he could be anywhere. Man on ledge is not Holmes he wears the costume Moriarity used to scare the children and that is what he has returned to Moriarity not the key code. Homeless (Holmesless) Network and Molly play the parts in the leap of death magic act.

Sherlock Holmes asks Molly (the coroner girl) for a favour knowing he would die, so he got her to take a dead body and put a mask of Sherlock on it. When Holmes jumps, there is a red bus parked underneath, filled with bags to soften his fall, and he had Molly dump a body when he would land. The reason why the biker pushed Watson over was so that he didn’t see the body switch. One can tell, because Sherlock jumps when there’s no one around and also because Watson checks for a pulse, which means that the body was dead, and not Sherlock knowing he would survive the fall.