1. If you have a book dedicated to you, you should probably read it. It's generally a nice thing to do. If a book is dedicated to your memory, try floating your ghostly presence towards someone who is reading the book, or become a poltergeist so you can manipulate physical objects. If you have gone straight to heaven, do not pass go, do not collect $200, see if you can order it online. Maybe Amazon ships there? I don't know, it might be pricey. (You know when shipping on a book costs as much as the book itself? That's annoying.) (ARE YOU READING THIS BLOG POST FROM THE ASTRAL PLANE? KNOCK TWICE FOR YES.)
2. It really is incredibly lovely to buy a copy of your friend's book when it is published. I understand if you are poor, though, so maybe just borrow it from the library and then tell all of your rich friends how wonderful it is. Yeah, I don't have rich friends either. Just yell about it on the internet.
3. If you have a friend who has a book published, and you read that book, and you think it's the worst thing ever written, and you value the friendship, try to lie convincingly when asked what you thought of it. You don't have to say you loved it if you didn't, but soften the truth a little. "It's not really my kind of book" is not really an acceptable answer. I think "I am so proud of you" is better, and not technically a lie (assuming you are proud).
4. That said, don't review your friend's book positively on the internet if you didn't actually like it or even read it. It's very obvious when someone's mates are boosting their ratings on particular sites. (Maybe a little bit of this is okay? I don't know, it's a slippery slope.) And don't get in arguments with people on the internet (generally a waste of time, but you know this), especially over negative reviews (it reflects poorly on the author. And you love the author, so you don't want that).
5. Don't ask how many books your author friend has sold. No author knows the exact number! If you obsess about these things you go mad! I actually have an amazing superpower where the lightning-bolt shaped scar on my head burns every time someone buys my book, but I'm bad at keeping track. Other unappreciated questions include "How much money have you earned?" and "Are you a bestseller?" How much money a writer earns is largely out of their control. You work really, really hard at the writing bit and at the promotional bit but that doesn't guarantee you're going to do well. There's a lot of hoping for the best.
6. Do not alert your author friend every time an awards longlist is released that they are not on, or every festival program they are not part of, or the success of other authors generally. They probably already know about these things. There are a lot of ways to feel lame when you are a writer, and I don't think writers require much help in that department.
7. Don't bring up the fact that they've been working on their book for two years, and that lots of other writers manage to bring out a book a year. It takes a long time, all right? You can't rush it.
8. Continue to encourage your author friend to leave the house at regular intervals and communicate with other human beings. (If the author you know is an extrovert, I feel they will be much easier to maintain a relationship with. I think they're a rare breed, especially among the novelists.)