Open your public facing SharePoint Online website. It should be something like yoursubscriptionname-public.sharepoint.com.
By default, your public facing website is showing you something like this

First of all, we should do something about those directions and contact pages. Just delete the pages that you do not want. For me, Contact us and Direction has no interest, as they don’t have much to do with blogging. Go to the page, press the PAGE butting, and then Delete Page. Confirm, and you are done.

The Abous us, page is going to become the About me page. Nice, huh?

Open About us, click PAGE, then Edit Properties, and change Name to About-me and Title to About me. Keep the rest as demo data, and click Save. Finally click EDIT LINKS and rename the link to About me. You could also move the Blog link to the left. It’s more logical I think. Press Save.

Now, we are going to change the default home page to the blog post roll. Open Site Settings, go to Look and Feel and press Welcome Page.
On the Welcome Page, press Browse…, select Blog.aspx, and press Insert, and then OK

You do not need the default page anymore, so you can now go to Site Contents and delete it if you like.
As the final task for now, we are going to change the Website title, and optionally the logo. Standing in your home page, klikk SITE, and Edit Title. Type something catching, and click OK

And now, you got your own Office 365 blog. In the nest blog post, I’m going through the process of styling the blog. Stay tuned 