Each game is meant to playable as a standalone thing, any direct storyline continuation from previous titles is covered in the game itself. Technically Ocarina of Time and Majora's mask are a pair with MM as the sequel, but either can be played alone with no real loss of context. MM does build on gameplay of OoT though.

It's not a spoiler to say that across the game series it's generally a plot about some reincarnation of the three central figures of Link, Zelda, and Ganon. There's often implied reincarnations of other characters too across multiple games, but that's mostly just callback fluff for fans. There's one game set first in the in universe timeline that sets up the impetus for the reincarnation cycle, and one game that splits the timeline into a few branches based off three different interpretations of the ending of that specific game.

The two main newest ones, Breath of the Wild and Tears of the Kingdom, are a two-fer as well, and are a new timeline or convergence of the split timelines depending on who you ask.

For a first time player, don't worry about it. Whichever game you play will give you what you need to know. Any understanding of the "grand series plot" just adds some extra oomph to scenes in later released games than OoT and MM.

Most Zelda games are completely standalone and can be played in any order without really having any overlapping story. I think technically Majora's mask is a sequel to Ocarina of time but you don't need to play them in that order.

Each game can stand on its own. Nintendo is well aware that its audience will always include children playing their first Zelda game on their first console.

If any of the games refer back to a previous one, it will almost always be Ocarina of Time. OoT depicts the origin story of the series' main villain, so the boss fight at the end of that game marks the "Year Zero" for the series kind of the way the Battle of Yavin does in the Star Wars fandom.

Because Ocarina of Time involves time travel, it actually forks the timeline into three paths: Link is defeated, Link defeats Ganon and the timeline continues from there, Link travels back in time to prevent Ganon from rising to power in the first place. Later a fourth branch was established: Prequels, set before the events of OoT.

At least one game is a fever dream, at least two games take place in other, faraway kingdoms, at least one game can be interpreted as a fever dream or a faraway kingdom, and then Breath of the Wild and Tears of the Kingdom seem to be a reboot of the series because ToTK retells OoT's story and retells it wrong.

There's an overarching storyline with some timey-wimey bits that I read at one point and have since forgotten. I haven't played all of them so maybe there are continuity assumptions elsewhere but both of the n64 titles can be played without knowing anything else about the series. MM complements OoT, but even they don't have to be played in release order to be appreciated.

To be fair to Nintendo, they painted themselves into a corner.

The first game was supposed to capture the feeling Myamoto had when exploring the woods near his home as a kid, so it has an excuse plot about collecting magical plot tokens on a quest to rescue a princess from a monster. It did well enough to get a very dissimilar sequel, because Nintendo also hates sequels. Myamoto always wants to do something new, he always resists making more of a good thing.

The third game, A Link to the Past, returned to the top-down dungeon crawl, but there was room on the cartridge now for some NPC dialog, so they wrote some backstory. And they got a little carried away becuase they wrote a creation myth, a deep backstory of the kingdom, a villain, and the design document of the rest of the series. The fourth game, Link's Awakening on Gameboy, is canonically a dream. It all happened in Link's head.

The fifth game, Ocarina of Time, is a prequel, they made a game out of A Link to the Past's fluff text. Fans went fucking nuts for it. The sixth game, Majora's Mask, is a game made on a strict one-year deadline, it has themes of constantly ticking clocks and impending doom. Write what you know, boys.

The Oracle games are side stories that don't effect the overall story, Wind Waker is the way it is because Myamoto went on a vacation to the beach and liked it, see also Mario Sunshine. Minish Cap is a distant prequel that takes place before OoT, and then Twilight Princess came out, made almost entirely to address the backlash against the cartoony art style of Wind Waker and to a lesser extent Minish Cap.

Nintendo sold the Wii on its motion control gimmick. Twilight Princess was a launch title for the game, but TP was designed for the Gamecube and they just mapped wiimote swipes to button presses. They took the rest of that long console generation to develop Skyward Sword with actual motion controls, and it was yet another distant prequel even predating Minish Cap.

It's the 2010s by now. Youtube exists, and fans are starting to make video essays about the sprawling, self-contradictory series and trying to form it into a cohesive whole. Detecting a merchandising opportunity, Nintendo releases Hyrule Historia, a nearly 300 page hardcover book that among other things contained the officially sanctioned timeline of events: The timeline splits into three separate parallel realities at Ocarina of Time, meaning some of the biggest entries in the series to date: A Link to the Past, Wind Waker and Twilight Princess, had nothing to do with each other.

One 3DS sequel to ALttP later that largely takes place in yet another alternate reality, and they come out with Breath of the Wild, which is deliberately nowhere on the timeline and contains details established in all three split realities, followed by Tears of the Kingdom which retcons even Ocarina of Time out of existence.

TL;DR: The story of the Legend of Zelda series is best summed up by its main character, Link, when he said "Hep! Hap! HEEEEEYAH!"