***** NOT A TEACHER *****
Congratulations! I think that you've done a great job.
(You) = the understood subject. A pronoun.
read = verb. (Imperative. That is, it's an order, command, suggestion, etc.)
a = adjective. (A newer term, I believe, is "determiner.")
book = noun.
a = adjective / determiner.
day = noun.
* "a day" in your sentence is being used as an adverb. That is to say, it modifies the verb "read."
As one of my favorite books would explain it, your sentence means something like: (You) read a book to the extent of a day. (In other words, you should read 365 books in a year.)
Student or Learner