DON'T favorite every tweet that mentions your book, unless you're tagged in it, you already follow the person, or someone you follow retweets it. It can come across as stalkerish, and it can sometimes be apparent that you're searching your book title.
But! If someone tweets positively about your book and tags you in it or someone you follow retweets it, then DO feel free to thank the person and/or favorite their tweet.
DON'T spend all your social media time sharing buy links, retweeting praise, talking about when your book comes out, etc.
DO take the time to interact with fans who have asked you questions or praised your book, and also talk about random things in your life. Readers like an author who is relatable, who maybe likes the same TV shows or music as they do.
As a general rule, DON'T read reviews. If you know you can handle positive ones with some criticism and you know the review is positive, read those. Otherwise, steer clear of them, even if they're tweeted to you. I as a writer know that unsolicited criticism isn't always fun to read. But reviews are there for publishers and readers, NOT for the author. You've already gone through rounds of criticism and editing.
Additionally, DON'T respond to any negative reviews, subtweet about them, and so on. Yeah, the criticism stings, but be mature and keep your thoughts to yourself. Rant to a parent, spouse, or trusted friend instead.
Finally, if you're going to respond to a review (hopefully a positive one), DO limit your response to something along the lines of, "Thanks for reading, and thanks for the review!" There's no reason to respond to any of the criticism they might've included, even if you think it's valid and realize that's something you need to work on in future books.
I saved the best for last.
DON'T STALK BLOGGERS. I don't care if he/she hated your book. If you start reading all her reviews, and checking out all of his social media sites, and subtweeting bitterly about her, and eventually try to find where she lives or his private email address or her phone number or anything she's chosen not to share for a reason, YOU'RE A STALKER.
The good news is, the vast majority of authors don't need to worry if they're stalking bloggers or not. They know better. But unfortunately, there are those rare few that show up and make the author community and blogger community look terrible as a whole.
Now, if you'll excuse me, I'm going to finalize my name change and application to the witness protection program.