Yes, after all these years, blogging is still very much a part of promoting your work. Most authors will tell you that it’s important for you to keep up a regular blog on your website, but it’s also important to reach out and expand your audience.
Becoming a guest blogger on someone else's page will open you up to an entirely new set of audiobook listeners. Just like with podcasts, you want to make sure to read the blogs you're interested in guest appearing on, before reaching out to the owner.
Think about ways that your guest blogging on their blog will be beneficial to both of you. Let them know why you want to appear on their blog specifically. Be genuine and create a lasting contact with them. If you have a solid readership on your own blog, you can offer to trade posts.
Make sure to give your blogger a copy of your audiobook too. If they know the material, they will most likely be more than happy to promote your guest post.
Beyond just website blogs, you can also team up with Twitter users to have Tweet chats where you are talking back and forth about your audiobook, interacting with listeners, and creating a solid foundation on Twitter.
YouTube interviews can be great promotional opportunities as well. Usually, if you aren't in the same area, you can go live or pre-record your interview with them. This will make for great marketing material as well.
Always make sure to go into these posts and interviews with something more than just a sales pitch. Offer the listener your expertise. Talk about the process, your inspirations, and even your goals for the future of your characters.
Always make sure to include your audiobook sample in the posts, as well as links to where they can download it.