What's explained in Myst
Who are you?
This is never explained in-game. I believe the intent is that the player character is you.
How did you get there?
You found a book, which the narrator (late in the game revealed to be Atrus) had intended to destroy, or at least get rid of. This book took you to the island of Myst, but with no route home. Touching one of these books is a one-way trip to another realm, a picture of which is on the page you touch to start the game.
This one-way trip mechanic is also how Sirrus and Achenar became trapped in their red and blue books. The island also has books that take you to other areas, where you can solve puzzles, but they each have a book that will take you back to Myst, the hub of this adventure.
What's explained outside of the first game
Who are you?
You are "The Stranger," a 19th century everyman who finds the Myst linking book. There's actually not a lot of backstory on the protagonist, period. There's some referenced material at the bottom of the linked wiki page for the Stranger, such as:
According to a Myst Guidebook, the Stranger found the Myst book in a San Francisco library. He read the book, which described perfectly an island, and saw the linking panel in the final page. This information can't be canon[.]
As it's indicated in parts of the lore that the game series takes place in the 19th century, so it's not really possible for the Stranger to be you (unless you're really, really old...).
In subsequent games, Atrus (and other characters) will speak to you as if you're the same person as the protagonist of Myst, so for the main game series it's assumed these adventures are had by the same person.
How did you get there?
To understand this, you'll need to understand a bit more of the lore. A lot of this is in Riven, (Myst's sequel) if you know where to look. However, Riven is also light on story for the most part. It wouldn't surprise me if you completed that game and were still confused.
I'll try to keep this as spoiler free as I can, but you should know that there may be spoilers here.
The worlds ("Ages") in the Myst series are "descriptive books" written by D'ni trained in the Art. In addition to descriptive books, the D'ni also were capable of creating "linking books" where touching the page would take you into the Age the book was linked to.
For the most part, humans and the D'ni did not interact, until the events leading up to the Myst series. By the time the series starts, the D'ni are mostly creatures of legend, and the books they authored are quite rare.
Owing to a conflict between Atrus and his father, Atrus fled to the age of Myst along with his family. He was afraid that if he left his Myst linking book behind, he'd be followed. Thus, he held the book over what he believed to be an infinite void called the Star Fissure. When he linked to Myst, the linking book he used fell into the fissure, putting it out of reach of those who would follow him and do him harm.
However, a couple of things happened he wasn't expecting. One was that his children eventually became tyrannical (somewhat because of his neglect), and they conspired to trap him and his wife.
Luckily, the other was that the Myst linking book was not destroyed. It is found by The Stranger, who arrives and (eventually) helps him resolve many of these conflicts.