Here is a detailed summary from nf user who saw the movie
The movie start by going back 41 years into the past, where Planet Vegeta is suddenly swarmed by dozens of Planet Trade Federation (PTF for short) ships. King Vegeta is made aware of their arrival and a mass of Saiyans (most likely upper class) go to greet King Cold, who had just exited his ship. At this point in time, the Saiyans had already been affiliated with the PTF and have been working under King Cold for a while, but the purpose of this visit was to announce that the old king was going to retire and give command to his young son, Frieza. This marks the birth of the Frieza era of the PTF and he gives the Saiyans 500 scouters as a gift. While demonstrating the scouter's functions, Frieza notices that there were 3 Saiyan snipers surrounding him from within the castle walls and he dispatches each of them before they can even react with a Death Beam each. Frieza then says that he's got high expectations of the Saiyans and leaves the planet.
Afterwards, King Vegeta visits an underground chamber in which a small number of soon to be Elite Saiyan children were being nurtured inside their incubators. King Vegeta claims that his son is showing remarkable growth and that he's got the potential of a genius. A few meters away, Broly is also found inside one of those incubators and the Saiyan personal informs their king that the child shows abnormal power. One of their scouters even breaks while attempting to measure Broly's power level due to his fluctuating power. Shocked and in denial, King Vegeta decides to send Broly away, fearing that he might one day not only challenge his son for the throne, but also become a danger to the universe itself. Therefore, Broly is soon extracted and placed inside a pod. Coordinates: Planet Vampa. An isolated planet devoid of human life. This doesn't go without catching the ear of Paragus and so he seeks audience with the king in hopes of changing his mind, struggle which turns out to be in vain. Angry and betrayed, Paragus vows to have revenge and leaves on a space ship with that Saiyan we see with him in the trailer (who happens to tag along) and goes after Broly. Their landing is rough, but they make it in one piece and soon go in search of Broly. The planet is full of those spider-crab like creatures and as the two Saiyans do their best to avoid them they eventually find kid Broly inside a nest, having devoured quite a few of them. After Paragus makes contact with his son he realizes that the child had turned into an Oozaru in order to ravage them (apparently there's a moon near Planet Vampa). This is when Paragus scans Broly and his power level as a kid is revealed to be 920. After that, Paragus attempts to leave the planet but it's revealed that their tough landing severely damaged the ship, making it useless. In order to save food, Paragus kills the other Saiyan so that only him and Broly remain and activates a distress call...
Five years after Frieza's visit to Planet Vegeta the scene changes to Bardock returning from battle. He's having a discussion with his fellow Saiyan pilot and is very suspicious of Frieza's order of all Saiyans returning to their home planet. Bardock theorizes that Frieza might want to kill them so he visits Gine and decides to send Kakarot away to Earth (where he'd be safe) just in case. While reluctant, Gine agrees to that and we have a nice Superman moment in which Bardock hold a crying Gine close to him while their son departs the planet in a Saiyan pod. I forgot to mention that Bardock asks Gine about Raditz and she says that he's been placed in the same team with Vegeta. On his ship, word about the Super Saiyan and Super Saiyan God legends have reached Frieza's ears, so he decides to eradicate the Saiyans together with Planet Vegeta in order to make sure that there's no possibility of those legends coming true. As Frieza launches his Supernova at the planet, Bardock is the only Saiyan that launches a huge ki blast at it in an attempt to try and do something. Obviously, this fails and he's engulfed by the huge fireball as it makes its way into the planet and completely annihilates it. Vegeta was on another planet, together with Raditz, Nappa and two other Saiyans. Nappa and the two other Saiyans are shocked to hear that "a meteor has destroyed Planet Vegeta" and they inform the Prince. Raditz says that they were lucky, while Nappa says that Vegeta supposedly had a brother as well (nice Tarble reference) and wonders what happened to him, to which Vegeta responds by saying that he doesn't care. Nappa then asks Raditz about Kakarot, to which he replies that he was a weakling so it doesn't really matter, but he does mention that he had received a message from Gine earlier in which she mentioned that she'd send Kakarot to Earth.
Time jump to the present day... Goku and Vegeta (Buu Saga outfit) are sparring on a deserted island, while Bulma with Bulla, Whis and Beerus are enjoying some food not too far away. After their sparring session is over, Whis asks Goku why he seeks further strength, to which he replies that the ToP opened his eyes to all the possible strong being out there (we get a picture montage of most of the ToP contestants, including Ribrianne, Kefla and the Pride Troopers). Whis then asks Vegeta what his reason for seeking further heights is, to which he replies with "Frieza's imminent danger". Vegeta realized that Frieza made some huge gains back in RoF, and now that he's alive again there's the possibility of him becoming even stronger and attacking them again. Goku then naively tells Vegeta that he shouldn't be worried since Frieza helped them win the ToP, and then they get into a funny argument in which Vegeta tells Goku that he's way too stupid to grasp reality. Bulma then receives a call from Trunks, who informs her that someone has stolen the 6 Dragon Balls she had collected as well as her Dragon Radar. Who could've done something like that? The answer of obvious: Frieza snuck two of his fodders on Earth in order to steal them and they were already headed towards the final Dragon Ball, which was located on the "arctic continent" as they call it. Since Beerus says that he's not interested and will stay behind, Bulma tasks him with babysitting Bulla until they're back.
Meanwhile, somewhere in space... we get introduced to Chirai and Lemo, who were tasked with finding strong people to join the Frieza Army. They happen to pass by Planet Vampa and decide to land there after the distress signal Paragus had set off 41 years prior is caught by their ship. A very old and frail Paragus crawl out of a cave after he sees them and rushes to their side. The two scan his power level and the old man is worth 4200, which still amazes Chirai and Lemo. Before they can finish talking a giant crab-spider attacks them, but before it can do anything to them Paragus calls for Broly who rushes in instantly and one shots the creature. Impressed by him, they try to scan Broly's power level, but their scouters can't process his power level. Shocked, they decide to take them back to Frieza HQ. Once there, Paragus and Broly meet Frieza. While Paragus is very polite and careful, Broly doesn't seem to give a shit and acts in a way reminiscent of Tarzan. Frieza informs Paragus that King Vegeta's son, Prince Vegeta, is still alive and well on Earth, which prompt Paragus to agree to share their strength for the sake of revenge. Next up there's a shower scene with Broly and he gets his new gear as well. Chirai invites the freshly showered Broly to their table in order to socialize, but a drunked Frieza fodder looking for trouble hits Lemo, which prompts a very annoyed Broly to kick his ass. Fearing that Broly is getting a little carried away, he pulls out his remote control and subdues Broly by activating his collar (which sends high voltage currents through his body in order to get him to forcefully calm down out of his rage tantrums). Disgusted by this performance, Chirai berates Paragus and manages to steal the remote control from his pouch without him noticing. A Frieza fodder calls for Paragus next, as Frieza seems to want to talk with him between four eyes.
Broly then goes with Chirai and Lemo somewhere quiet and they begin to bond. Broly explains that the green fur he's wearing comes from his very first friend. Planet Vampa displays two kind of creatures: the spider-crabs, and some gigantic green fur long necked dog-like creatures that live within the craters found on the surface of the planet. As a kid, Broly trained by continuously dodging the attacks of one of these green furred creatures, and by repeatedly doing so they became friends. One day though, Paragus attacked this creature, severing one of its ears. After that incident, the creature stopped interacting with Broly, and a saddened little B decided to wear the fur of that severed ear around him so that they'd always be together. After hearing this story, Lemo says that Broly is a really pure being, to which Chirai adds that she thinks Broly doesn't really want to fight, but instead is being used as a tool by his pathetic father in order to exact some vengeful agenda. They say Broly should ditch him, but the big guy says that he won't disobey his father.
Meanwhile on Earth, Bulma departed towards the arctic continent together with Goku, Vegeta and Whis. They ask why Bulma had been trying to collect the DBs, and she reveals that her wish is to become 5 years younger. This joke is a direct contrast to Frieza's wish (also a gag), which is revealed to be him wanting to grow 5 centimeters taller. In the meantime, the two Frieza spies have manged to find the last Dragon Ball and they call for Frieza's arrival on Earth. As old enemies meet once again, Frieza introduces Paragus and Broly to Goku and Vegeta as another group of surviving Saiyans. Neither Vegeta nor Goku care about that and they hasten Frieza to return
