I read this because I heard that it was a pretty influencial book in terms of the great tragedies that were written after it by the likes of Shakespeare and Christopher Marlowe. This is no where near as good as anything either of those two produced though.
The plot is this: Horatio is murdered by Lorenzo and Prince Balthazar so that Balthazar is clear to marry the woman that Horacio loves, Bel-Imperia. Hieronimo, father of Horatio is understandably upset at these events, and swears revenge upon the two murderers. This he eventually achieves, and in the age old tragic tradition almost every character ends up dead by the final scene.
The plot is decent enough, but for me it's all rather crude. With the exception of Hieronimo, none of the characters are really developed, and the language seems rather flat and even clumsy at times. If you read this and then any Shakespeare it would make you appreciate just how beautiful the poetry of Shakespeares writing is, and also how life like his characters are when compared to those of Kyd.
All in all I can't strongly recommend this to you, it's alright and it's entertaining enough, you probably wont hate it, but there are lot better plays from the time you can be reading, like King Lear or Dr Faustus, this is average, nothing more.