Do slyly pull your book off the bookstore shelf and prop it up prominently with its cover facing out. This is OK because it is still kind of cute, and besides, freaking everybody else is doing it.
Do not make up a dozen fake usernames on Amazon and other book-reviewing websites and post eerily similar glowing reviews of your book à la "Elsinore Periwinkle takes on the subject of alcoholism among upper-class toddlers with astounding vigor and mind-blowing insight. Elsinore Periwinkle has written the greatest book since ever." If you are ever found out, you will be shamed so mercilessly that the prick of ten thousand daggers would feel therapeutic in comparison.
Do encourage your readers to write an *honest* review of your book on Amazon or other sites. Having a decent number of reviews, even if some of them are ambivalent, makes your book look interesting and talked-about, as opposed to obscure or not worth reviewing.
Do not allow your well-meaning mother or BFF to create a dozen fake accounts on Amazon and various key message boards and post glowing reviews of your book, thinking it will help you. This is called "astroturfing" (ten points to the first person who can tell INTERN why) and while it can seem like a brilliant idea (especially to a mother or BFF who is unfamiliar with internet etiquette) it will destroy your credibility more savagely than the wrath of ten thousand polecats.
Do try your hand at writing a press release and/or press kit for your book, even if your publicist is taking care of those things. Having a book published is a great excuse to learn how to write killer sales copy, which could come in handy some day if you ever want to do freelance stuff.
Do not try your hand at any brilliant and ingenious publicity stunts without telling your publisher. The best time for them to hear you're going drunken sky-diving with a pair of alcoholic toddlers is *before* you step into that plane, not when it's front-page news and you're in jail.
Do go for the things that will give you the most bang for your buck. Two hours spent making an incredible author website are worth twelve hours spent painstakingly crafting and pitching an article that will appear in an obscure journal and be read by no one.
Do not try to promote your book in Mongolia. Mongolia doesn't like you, and is probably laughing at you right now.