it's been 3 years since the Enterprise has been exploring deep space and Kirk is bored because - wait for it - deep space is just full of empty space.
It brings him down and depresses him and he's not much of a diplomat so being diplomatic bores him. So he puts in for a desk job when they stop at a supercool new space station (which is so huge, it makes you wonder how fast they can build such places in the future) which is completely totally not his style at all. While there, a victim shows up and needs help rescuing her crew from a planet in a nebula where they crashed. Kirk agrees to take her to the planet since the Enterprise has the best direction sensing.
They arrive and get attacked by weapons and ships that can get completely inside their shields. The Enterprise is boarded and the bad guys - who seem to number in the tens of thousands - kidnap all the crew while the leader is looking for a doohicky that was part of their last failed diplomatic mission that the crew kept as a souvenir as opposed to returning it. How the bad guys found out about it is anyone's guess. The ship is then destroyed and the crew scattered over the planet in life boats which then the bad guys capture. Except they're scattered within a mile or so of each other.
The bad guy leader seems to want to talk to someone besides the 10,000 man army he has so he drags Uhura everywhere and explains everything that's going on to her, so the audience doesn't get lost. Then our heroes manage to find each other and with the help of a motorcycle that's nearly 100 years old and still uses wheels, the ignition of the 'fuel' the Enterprises uses, and good ole rock n roll they escape and defeat the bad guy, who turns out to be a Federation officer suffering PTSD, the side effects of an alien technology and a killer complex who really needed a pysch eval before the Federation gave him a starship to command. His big plan is to kill the people he thought abandoned him...
That's it. That's the big story. Like the 1st Star Trek reboot, it's one man with an agenda who goes to A LOT OF TROUBLE for revenge. Yes, it's another revenge story.
My sister who was with me said, "It looks like a nice planet. Pretty, plenty of water, forests and fresh air. You'd think they'd start building houses and farming over the years. Settle down, you know?"