Movie Spoilers. Do not read if you don't want to know. This is by someone who saw the recent trailer:

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The movie opens with an alarm going off. Camera pans over to a couple waking up in bed. I can't remember the characters names, off hand. The man gets up and goes to his window. He looks out and the screen reads "London" and the star date. We then see a pedestrian aircraft pulling into an old London brick building, which we find out is a hospital. The outside is old London, but inside we see future technology such as antigravity stretchers. Cool! The couple is shown crying over a small girl in a hospital bed. She looks sick and is balding.

The scene then shifts to the father going out side, and as he is looking morosely out at the city you hear "I can save her."

the father goes "what did you say?"

once again, mystery character says "I can save her."

then, the father asks who the mystery man is, and the camera turns to zoom in... On Benedict climber batch- who does not reveal his name.

Scene shift to the red vine planet we see in the trailer. Jim is shown to be running from the natives. A big monster pops up out of the bushes and Jim shoots it with his phaser. Bones pops up behind the monster and says "dammit Jim, you just shot our ride," and something else funny. They both start running as the natives, who look really creepy, start to gain on them.

Scene shifts to a shuttle craft that is inside the volcano on the planet. Spock is getting suited up in the red lava suit from that early leaked picture.

The atmosphere is urgent, the volcano is set to explode and Spock needs to get in there and detonate this machine to stop it. Uhura is helping him suit up, and she keeps flirting with him for gods sake. She kisses his visor, and makes a little joke along the lines of "sure you don't want me to go instead?" Spock had a funny response. In his completely flat Vulcan way he goes "that would be illogical as I am already dressed" or something to that effect. Uhura chuckles at him and wastes more time with her little be safes and that jazz. Even sulu was like shut up, he needs to go. It may just be me, but Spock wasn't really into her flirtyness either. I can see this being a problem for the duo in the future. Uhura seems emotionally compromised where Spock is concerned.

Anyway, Spock zip lines out of the shuttle to go down to the volcano surface... Only the shuttle craft starts to overheat and they want to pull back and abort the mission. Spock says no, if he doesn't complete the mission the species on the planet will go extinct. They don't listen to him and start to pull back... But Spocks zip line snaps and he plummets into the volcano. Luckily he lands on a non lava surface. He makes a funny line, something to the effect of "it may be illogical, but I am still alive." Anywho, the shuttle has to get out of there and Uhura is freaking out And promising they will find a way to save Spock.

Cut back to Jim and Bones who are still running from the natives. They distract the natives then plunge off the cliff into the ocean. We see them swimming under water, and the enterprising young men music starts and you see thAt they are swimming towards the enterprise which is sitting on the bottom of the ocean area. They get inside through a hatch, and the first thing Jim asks when he is inboard is ...
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"is Spock back on board yet?" woo for the concern! I was so happy! Anyway, Scotty is all like no, and he was complaining about the damage to the ship from the water and all that.

We shift to the bridge, where Kirk tries to contact Spock. Spock says he almost has the volcano detonator ready, and advises that the enterprise leave him there. Kirk says no, they will move the enterprise close to the volcano to save him. Spock says no, because that will violate the prime directive... Jim is all like "I will save you," and Bones says " dammit man, we're going to save ya." just like in that episode of TOS! Spock then says no, "the needs of the many outweigh the needs of the few." then Spock kneels down, takes a breath and closes his eyes. He spreads out his arms like he is waiting for death. Cut back to the bridge, where Jim asks Bones "if our roles were reversed, what would Spock do."
Bones responds "he'd let you die."

Cut to darkness, and a gorgeous title sequence. Then we get a montage of scenes from the teaser, maybe some new things but it was really fast. The Japanese footage was at the end of the montage.