I think they're all more or less the same.

To read it through means to start at the beginning and to keep reading until you reach the end. I don't think it describes exactly how much detail you should take from the reading. Since it is a phrasal verb it's meaning has a tendency towards slackness and informality, so it may mean read all of it, but not carefully. Read it carefully. That's one end of the spectrum. Go through it at home, but don't worry if you don't understand everything at first reading. That would imply to me that you have to read it all but not really carefully. Skim through it. That means glance at each page and read the bits that you feel like. Does that answer things for you? I have to add a comment on how silly English can be: it used to be that the word peruse in English meant to read in detail, but in the last half of the last century people started using it to mean to skim through it. And now peruse can mean either. So its sense has been destroyed.