The D'ni originated from a world called Garternay, where they were known as the Ronay. Their culture developed its own language and its own numbering system, and they had knowledge of how to access ("link to") alternate worlds ("Ages") through special books; they called this knowledge "the Art of Writing." Over ten millennia ago, Garternay was destroyed. Its refugees wrote several Ages to escape the destruction; one group's leader, Ri'neref, wrote the Book of D'ni, which linked to a huge cavern under North America. (The Book of D'ni in the story's sense should not be confused with the actual novel, Myst: The Book of D'ni.)
Atrus's childhood home (See the Book of Atrus) was a place in New Mexico known as The Cleft. It's a large chasm in the side of an inactive volcano. As it is described (and later seen in Uru: Ages Beyond Myst), the Cleft has rooms carved into each side of the cleftwall, with several rope bridges spanning the gap. The caldera of the volcano itself houses the entrance to a long series of tunnels, eventually leading to the D'ni cavern.
Over 200 years ago, D'ni was beset with a great catastrophe that led to its fall. Again the D'ni had to escape to other Ages, leaving their great underground city in ruin. (See the Book of Ti'ana)
D'ni, The Art, and D'ni's Ages were rediscovered by a human, Elias Zandi, in 1987. He founded the D'ni Restoration Federation to revive the city. It later spawned the D'ni Restoration Council (DRC) which now passes on part of the exploration to the players of Uru: Ages Beyond Myst.
While the Myst games and novels are our main sources of knowledge of the D'ni, some events and principles are not portrayed as they "actually" were. For example, we have learned from Cyan that the Prison Books in Myst and Riven are not part of the actual history; rather, they are elements of artistic license, introduced to simplify gameplay.
In the D'ni canon, the games (except Uru) and novels actually exist as fictionalized histories. In Uru, you can even wear Myst and Riven T-shirts. Uru itself, however, takes place in the present day; as such, it is not historical, and therefore its events are part of the D'ni canon.