It takes the form of a lost Shakespeare play (based on Holinshed's very prosaic account of Arthur's reign) preceded by a much longer, predominantly tangential and autobiographical, introduction from the novelist whose father, a convicted forger, "discovered" it.
The unresolved question, of course, is whether it's "genuine" within the fiction, with plenty of clues to point one either way. Which is obviously very clever.

But I found the self-obsessed narrator's life story had almost completely alienated me by the time I reached that point.
(This is the opposite approach to Pale Fire, where the monomania and self-obsession of Kinbote's notes is contrasted with the generous humanity of Shade's poem, but crucially the reader gets to read the latter first.)

Unfortunately, I wasn't interested in the framing narrator, his daddy issues, his sexual incontinence, or his petulant opinions on Shakespeare. And since the play's Arthur is written to reflect him, I wasn't very interested in him either.
The question of authenticity, especially as applied to Shakespeare, is intellectually interesting, and there's a lot about the treatment of it here that's very clever.

The issue is whether a play's value is intrinsic or derives from the idea that Shakespeare wrote it.
But since we know full well that the novelist Arthur Phillips wrote this one, it's a spurious question.
It's like the readers of Pale Fire who speculate that Shade wrote Kinbote's bits or vice versa, and in doing so collapse the whole structure. Guys, Nabokov wrote all of it.

Anyway. There's a lot to appreciate here, from an intellectual point of view, but it's emotionally alienating and it's not as much fun as it should be. Which is a shame.