There are a total of 7 Black Books. Reading each one will take you into the realm of Apocrypha. Make your way through the various twisty paths and puzzles you encounter here, and you'll eventually reach another book at the end of the area. Read this book to gain a special power and return to Solstheim. (Some of the books will give you 3 options for a power to choose, so make sure to look at the green orbs hovering above the book for details on each one!)
Two of the Black Books will be encountered during Dragonborn's main story, so you'll need to track down at least 3 others. Most of the other 5 are linked to sidequests, but here are the locations of them all:
Waking Dreams - Main story (You pick up this book early on, but it doesn't actually count towards this achievement until you've finished the At the Summit of Apocrypha quest.)
Epistolary Acumen - Main story
Filament and Filigree - Kolbjorn Barrow (end of Unearthed sidequest)
The Hidden Twilight - Tel Mithryn (After finishing several sidequests for Neloth, he'll give you a key to the room containing the book.)
The Sallow Regent - White Ridge Barrow
The Winds of Change - Raven Rock Mine (You'll pick this one up since it's in the same area as one of the words for the Dragon Aspect shout and achievement.)
Untold Legends - Benkongerike