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.

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.

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.