Is there any explanation for the Island of Myst or how the player arrives there?

I seem to remember that The Stranger finds the Myst book in the stacks at the Chicago San Francisco Public Library. I don't remember where I read this, but I think it was in the separately-published hint guide.

How the book arrives in the Library is explained (sort of) in Riven: The Sequel To Myst.

Atrus, the man you meet at the end of Myst, once lived with his wife Catherine and his father, Gehn. All three were able to write Linking Books (books which link to other worlds). At some point, Atrus and Catherine realize that Gehn incorrectly believes he is creating the worlds in the books rather than simply opening doorways to already existing worlds. Atrus and Catherine determine that Gehn is a danger to the inhabitants of these worlds, and they decide to trap him on Riven, a world without the ink or paper necessary to write Linking Books. Riven contains a location known as the Star Fissure, a portal which (unknown to anyone) leads to Earth. Atrus and Catherine destroy all but one of the Linking Books on Riven, and then escape to Myst through the Myst Book, holding it over the Star Fissure so that when they link through, the Book will fall into the Fissure and be lost. Their plan succeeds and Gehn is trapped on Riven, while the Myst book drops through the Fissure to Earth, where it is eventually found and used by The Stranger.

Atrus mentions this event in his opening narration:

I realized the moment I fell into the Fissure that the book would not be destroyed as I had planned. It continued falling into that starry expanse, of which I had only a fleeting glimpse. I've tried to speculate where it might have landed, but I must admit that such conjecture is futile. Still, questions about whose hands might one day hold my Myst book are unsettling to me. I know my apprehensions might never be allayed, and so I close, realizing that perhaps, the ending has not yet been written.

Little to no detail is ever provided about The Stanger. This is intentional, as it allows the player to experience the world as themselves, rather than forcing the player to take on an unfamiliar and therefore less immersive role (such as a space marine, theoretical physicist, or black Scottish cyclops).

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.

This information is explained in the games instruction manual, but can be found at other sources as well:

The game's instruction manual explains that an unnamed person known as the Stranger stumbles across an unusual book titled "Myst". The Stranger reads the book and discovers a detailed description of an island world called Myst. Placing his hand on the last page, the Stranger is whisked away to the world described, and is left with no choice but to explore the island.