However, for anyone who's never seen Dragon Ball or hasn't tuned in since the Toonami runs when they were ten, it'll be hard to follow what's going on besides the fact the characters can fly and shoot energy (ki) blasts at each other.
Based on characters seen in the trailer, and without spoiling too much, here's a basic guide of what anyone needs to know before watching Dragon Ball Super: Broly.
Saiyans
An ancient warrior race based on the planet Vegeta. There was also a King Vegeta and his son, Prince Vegeta because it happened to be such a cool, hip name.
Whilst being similar to humans, they’re natural born fighters, age half as fast and have monkey-like tails. These tails cause them to temporarily transform in the presence of a full moon to an Oozaru: a giant great ape that shoots laser beams out of its mouth Godzilla-style. As well as being capable fighters, they were basically space pirates: finding a decent planet and killing its inhabitants before selling it for profit like murderous estate agents. This went on for a long time until they were forcibly employed under the galactic tyrant, Frieza, who used the Saiyans as mercenaries to conquer planets for him instead, spreading his rule. As the Saiyan army continued to grow in strength, Frieza began to fear the prophecy of the Super Saiyan: a 1000 year old tale of a golden Saiyan of legend that would be powerful enough to defeat him.
Planet Vegeta
Fun fact: Like the name "Vegeta" implies, Saiyan names are puns on different vegetables. For example, Kakarot is based on carrot, Broly on broccoli and Raditz on radish.
Goku
The lovable Saiyan who is the main hero of Dragon Ball. With Saiyans as young as babies being sent off-planet on missions, the same was done to Goku as a new born, being given the Saiyan name Kakarot. He was blasted off to Earth shortly before the destruction of planet Vegeta.
A while after landing on Earth and being adopted, he fell into a ravine and fell head-first onto a boulder, irreversibly altering his violent Saiyan tendencies to become a good-hearted young man. His Saiyan tail was permanently removed so he wouldn't turn into a giant monkey and kill everyone every few weeks.
Mastering martial arts and becoming stronger under various masters, he's saved the Earth (and the universe) various times. After a long battle and at the loss of his best friend (being murdered by Frieza in front of him), Goku's overwhelming anger consumed him, transforming into the first Super Saiyan. Then defeating Frieza, Goku avenged the genocide of his fallen race.
With his wife, Chi-chi, Goku also has two half-Saiyan sons: Goten, and his eldest, Gohan, who was named after Goku's adopted father.
Over the course of Dragon Ball Z and Dragon Ball Super, Goku has unlocked various colourful transformations, each being stronger than the last:
Kaioken: The red one. It multiplies speed and power by a certain number of times according to Goku's will. Using the Kaioken for too long carries the risk of instability and eventually crippling the user.
Super Saiyan: The original gold one. There's also a Super Saiyan 2 and 3 (still gold with longer hair) but it's simpler to just roll them into one.
Super Saiyan God: The red one that also colours the hair. The use of Gods is a major element in Dragon Ball. In order to prevent the God of Destruction, Beerus from destroying the earth, Goku and the other Saiyans abused a loophole in the lore in order to have his Super Saiyan form infused with the power of a God.
In addition to the power boost, it also adds the most speed amongst the Super Saiyan forms, even making Goku seem leaner during the transformation.
Super Saiyan Blue: The blue one. It's the result of combining the powers of a Super Saiyan God with the original Super Saiyan transformation. Also, it was orignally called Super Saiyan God Super Saiyan because it's fun when anime powers are given over-complicated names.
Ultra Instinct: The Silver One. A non-Saiyan transformation that was previously only achievable by deities. Together with the power boost, it allows Goku's body to react on it's own, giving him the ultimate reflexes and speed.
Vegeta
The Saiyan prince who was off on a mission when planet Vegeta was blown up by Frieza. In order to keep Vegeta loyal and on a short leash, Frieza lied by saying his home world was hit by a meteor. That is until years later when Vegeta hears about Earth's Dragon Balls: seven wish-granting orbs that summon a mystical dragon and grant whatever wish you want. Going to Earth to wish for immortality and destroy the planet, he eventually fought and lost against Goku and his friends, losing his Saiyan tail in the process.
As the series went on, Vegeta gradually progressed from villain, to anti-hero and then ally, helping Goku and co. save the Earth several times. Nevertheless, he holds an everlasting rivalry with Goku, always being frustrated he's never been able to surpass him.
Vegeta's been able to achieve transformations in the same way as Goku: unlocking Super Saiyan, Super Saiyan 2 and Super Saiyan Blue.
In terms of family, he has an anime-style blue-haired human wife, Bulma. Vegeta also has two half-Saiyan kids: a son, Trunks and a baby girl, Bulla.
Frieza
The Galactic dictator whose transformations range from horned space lizard to an alien Oscar. After being defeated by Goku and being killed a couple of times, Frieza was brought back to life at the end of Dragon Ball Super, as a reward for helping save the universe, despite still wanting to eventually kill Goku and his loved ones.
Fun fact: members of Frieza's race are given names which are puns based on the cold and refrigeration equipment. His is based on a freezer. His brother is called Cooler, his dad is called King Cold and his ancestor was named Lord Chilled.
Bardock
Goku's Saiyan father. Whilst on a Saiyan mission of kill-everyone-and-conquer-the-planet, Bardock has a vision through one of the inhabitants he killed, foreseeing Frieza's betrayal of the Saiyans. Failing to convince his fellow Saiyans to band together in rebellion against their dictator, Bardock decided to take the fight to Frieza himself, killing many of his underlings in the attempt.
Despite failing in preventing the murder of his race, Bardock's visions showed his son, Kakarot, escaping in his Saiyan space pod towards Earth and growing up to become the great warrior who would avenge his people.
He also had an older son, Raditz but he's not that important in the grand scheme of things. If anything, he may only get a passing reference or brief appearance.
Beerus
The universe's God of Destruction: whose job it is to destroy planets that aren't performing up to his standards, in order to maintain balance with other Gods who create and preserve them.
Waking up from a long slumber and being caught up on the defeat of Frieza, along with Goku and co.'s other exploits, Beerus visited Earth. With his short and petty temper, Beerus almost erased the planet from existence. After Goku fought him to an almost-stalemate as a Super Saiyan God, Beerus became a reluctant mentor to Goku and Vegeta, allowing them to be taught on his home planet. Him and Whis keep coming back to Earth for free food after falling in love with the planet's cuisine.
Whis
An angel who like all of his race, is an attendant to the universe's God of Destruction. Following Beerus' fight with Goku, he took on Goku and Vegeta as students to teach them new abilities. In addition to Ultra Instinct, Whis has many abilities that you'd expect of an anime angel that services a deity, including teleportation, resurrection and manipulating matter and time.
Broly
A newly emerged Saiyan, he's the anger issues-rich titular antagonist of the new film. This is a unique section given that the Broly here is a new incarnation of one from older Dragon Ball Z films.
Up until now, all of the Dragon Ball films have been completely non-canon (not part of the series timeline) and Broly is no exception. Dragon Ball series creator, Akira Toriyama, decided to change all that by giving him a complete redesign and write his own canon story.
In the original 1993 film, Dragon Ball Z: Broly – The Legendary Super Saiyan, Broly held a deeply embedded hatred for Goku since birth, being born around the same time and being continuously irritated by Goku's repeated crying in the Saiyan maternity ward until it became a trigger for his insanity.
Original 1993 version of Broly.
With some Saiyans being able to have their potential read from birth, Broly's immense power as a mere infant was one found never to be seen amongst his race. Being an apparent threat to King Vegeta, an assassination attempt was made in the maternity ward, stabbing baby Broly in the belly and beating his father (Paragus) to near death when he came to his son's defense. They both survived.
Luckily escaping the planet with his father, Broly survived the genocide of his race. Over the years, being consumed by an overwhelming rage all of his life, Broly transformed into the Legendary Super Saiyan, destroying planets all over the galaxy out of sheer anger. Lacking the ability to control those mental health issues, Broly would grow stronger the more emotional he became, even throwing Goku around like a rag doll. It seemed like only sheer luck he was eventually killed by Goku and his sons.
Rebooting his backstory and character completely. Going from a topless, bipolar space-Hulk and more of a seasoned warrior, Broly appears to be alot more fleshed out whilst stilling retaining that force-of-nature-monster trait that terrified Goku and co in the non-canon films.