A Memorable Day

Following the defeat of Khan Noonien Singh (see Star Trek II: The Wrath of Khan), the USS Enterprise limps back to Earth, heavily damaged from the battle. Once there, Admiral James T. Kirk is informed that the obsolete vessel's days are over (it is stated to be 20 years old, but official production timelines place it as about 40 years old, with Kirk's command of the Enterprise being about 20 years); it won't be refitted, but will instead be retired, and its crew reassigned. Meanwhile, Dr. Leonard McCoy exhibits strange behavior, somehow related to the deceased Captain Spock. He even seems to be channeling both Spock's behavior and voice. 
Simultaneously, Kirk's son Dr. David Marcus and Lieutenant Saavik are now on board the research vessel USS Grissom under the command of Captain J. T. Esteban to explore the Genesis Planet, created when Khan detonated the Genesis Device. While conducting sensor studies of the planet, Saavik detects an unidentifiable life form. Dr. Marcus asks Saavik to conduct a close range scan of the area and they discover Spock's burial tube. Dr. Marcus speculates that Spock's burial tube must have soft landed because of fluctuations in the gravitational field of the Genesis planet during formation. After a request to beam the life form on board is denied, Captain Esteban permits Saavik and David to transport down to the planet's surface to investigate the sensor readings. While there, they discover, much to their shock, that Spock's body has been resurrected by the Genesis effect, although his mind is no longer present and he operates on a purely child-like level. Marcus, pressed by Saavik, admits that he used unstable "proto-matter" in building the Genesis device to solve "certain problems". Without it, he claims that the Genesis Project could have been delayed by years or would have never been completed at all. The unstable matter puts the planet in a state of accelerated evolution that will conclude with its premature destruction within a few hours. 
Unknown to them, a Klingon commander named Kruge has intercepted information about Genesis and becomes interested in it (for much the same reasons as Khan: as a weapon). He travels to the Genesis Planet to learn its secrets after stealing additional information related to it. 
Spock's father, Sarek, visits Earth and discovers, with Kirk's help, that McCoy possesses Spock's "katra" (soul). Both his katra and body are needed to properly lay him to rest on his homeworld Vulcan; without swift intervention, Spock's consciousness will overwhelm McCoy, and he will also die. Disobeying direct orders prohibiting anyone from visiting the Genesis Planet, Kirk reunites with his bridge officers and goes through a series of highly unorthodox events such as Uhura charming the watch officer (locking him a closet), Kirk and Sulu springing McCoy from the Starfleet jail, Scotty hacking into the Starbase security system to open the massive base doors so the Enterprise can escape, and secondly disabling the pursuing USS Excelsior's "transwarp drive", by removing several circuits. 
Kruge arrives at Genesis first, accidentally destroying the Grissom with all hands (save for the landing party). He then summarily executes his weapons officer responsible for the Grissom's destruction; Kruge wanted prisoners. His crew locates and captures the scientists on the planet: David, Saavik, and a now-teenaged Spock. Kirk and the skeleton crew of the Enterprise arrive, unaware that the Klingon ship and its crew are cloaked nearby. Unable to hail the Grissom, the Enterprise crew suspects the presence of a Bird of Prey and are able to strike first, hitting the Klingon ship as it de-cloaks. In the ensuing battle, the Enterprise severely damages Kruge's ship! On Kruge's ship, the chief engineer tells Commander Kruge "Engineering to bridge, antimatter containment is failing!" Kruge says "Can you vent the antimatter?" The chief engineer says "Negative, my Lord! Warp core breach in 3 minutes!" Commander Kruge says "This is Commander Kruge! All hands to the escape pods! Abandon ship!" He then tells his men "You heard my order!" Kruge's men leave the bridge to get to the escape pods! Maltz says "What are you doing, my Lord?" Kruge says "I'm buying as much time as I can so that Emperor Palpatine can arrive in time to save you!" He then tells Maltz "Get out of here now!" Maltz says "Yes, my Lord!" and leaves the bridge! Kruge's men get to the escape pods and escape the Bird of Prey! Kruge stays behind, sacrificing himself! 
Torg, Kruge's first officer, watches as the Bird of Prey explodes with Commander Kruge on board! The Enterprise rescues the Grissom's landing party and escapes Genesis just as the Genesis Planet explodes! The escape pods from Kruge's ship are drifting in space! Just then, Maltz sees something! It is an Imperial Star Destroyer! Emperor Palpatine, the ruler of the Galactic Empire, is on board! The Klingons are relieved! Help has arrived! 
The Emperor's Star Destroyer brings the escape pods from Kruge's ship aboard! Emperor Palpatine tells Torg and Maltz "I am glad to see that you are safe! And I honor your courageous commander's heroic sacrifice!" Torg says "Thank you, Emperor Palpatine!" The Emperor says "In honor of Kruge's heroism, I will make any ship bearing the name Qel'poh the flagship of the Galactic Empire!" Maltz says "That's a good way to honor Commander Kruge!" The Emperor then took Torg, Maltz, and the Klingon ship's crew back to Qo'nos! 
Jacqueline, Chris Cochrane's beloved friend, played her piano and sang "My Heart Will Go On" for Chris! Jacqueline was accompanied by her rock band and by an orchestra! "My Heart Will Go On" was, of course, Chris's favorite song! Jacqueline sounded beautiful! She sounded good! Chris was very happy!