As a general rule most Zelda games are stand-alone stories: the same character names show up in all of them, and similar events, and they're set in a shared world (sort of), but each is set at a different point in the history of that world, and whilst the characters may have the same names they are generally not the same people.
With that in mind, and for the benefit of anyone who cares I thought I'd do a round up of all the Legend of Zelda games currently available to play on the current and previous generation of Nintendo consoles: which is to say the Wii, WiiU, New 3DS, New 3DS XL, 3DS, 3DS XL, 2DS, DSi, DS-mini, and DS. In no particular order, they are:
- Ocarina of Time 3D is a remake of Ocarina of Time for the 3DS family (including 2DS, 3DS XL, etc ...). This game is entirely stand-alone. No previous Zelda game is needed to understand it, and any relations between it and other games are really in the form of Easter Eggs. It's generally regarded as one of the best videogames of all time, and certainly regularly gets voted best in the series (though I disagree).
- Majora's Mask 3D is a remake of Majora's Mask for 3DS. Technically this one is a direct sequel to Ocarina, although the plot has little connection, it's just that the main character is the same. Still, the thematic similarities mean it's probably best to wait and play this one after Ocarina.
- Twilight Princess is a Wii original title (though a version for the game cube was released) which will play on a Wii-U provided you have a Wii remote. It's likely the darkest of the series, with a strong theme of ambiguity and ... well ... twilight. It was my first Zelda game, and I love it dearly, it's also completely stand-alone except for easter eggs, theoretically being set centuries after Ocarina.
- Skyward Sword is the only Wii exclusive instalment of the franchise, and requires the Wii motion plus or Wii remote plus to play (and will run on a Wii-U with those). It's an absolutely brilliant game, far and away my favourite computer game of any sort, and so I tend to feel quite sad that as a title released in the final days of the Wii it got very little attention. Unlike other games it makes extremely good use of the motion plus high quality accelerometers in the controller and maps sword movements directly to the movements of your hand. As a result of this it's one of the fastest and most dynamic games I've ever played: and one which very much rewards skill in the handling of the controls. It's also entirely stand-alone, theoretically being set centuries before any of the other games.
- Windwaker HD is a Wii-U remake of Windwaker, originally for the GameCube (and playable on a Wii). It's a fun piratical game, quite different in setting and feel from the more Ocarina influenced titles. Again, except for easter-eggs it's entirely stand-alone.
- Phantom Hourglass for the DS (and playable on the 3DS) is a direct sequel to Windwaker, and, to my mind, rather frustrating due to having to repeat the same dungeon multiple times in order to get through fast enough.
- Spirit Tracks also for DS is based on the same engine as Phantom Hourglass but is more of a standalone title: in theory it happens centuries after Hourglass, and a few references are made, but nothing important relies on knowledge of any previous games. This one has trains ... which should really be enough to make you want to play it by yourself.
- Link Between Worlds for 3DS is, technically, also a sequel, to Link to the Past, a very old game that is still highly regarded. I've never played Link to the Past and had no issues with Link Between Worlds, but I will caution any readers that it is a very old-school style of play. Still it makes extremely interesting use of the transition between 3D and 2D modes, which is pretty different, and rather cool, and probably means you'll be missing out on some things if you play on the 2DS. Its place on the timeline would theoretically be somewhere long before Ocarina, but still long after Skyward Sword, but as with most Zelda games this is not at all important.
In principle the whole timeline thing can actually get very complex, since technically the timeline branches due to time-travel shenanigans during Ocarina, but honestly it's of no interest to anyone whilst playing the games, and just a bit of a curious oddity to get geeky about elsewise.