Deploying to Azure is a really simple way to get up and running.

The first step is to set up a new Web App which can be found under App Services in the new Azure portal. Once you have the web app set up and configured, you can push your files to Azure in a number of ways. The exact mechanism isn't really important, but I've found SFTP works well. You can find your SFTP login information on the Overview page for your new web app. Just use any FTP application (like FileZilla) to connect to the given server using the given credentials. Once you're connected, upload the contents of the Wyam output folder to the /site/wwwroot folder in your Azure site (don't upload the Wyam output folder itself, just everything that's underneath it).

One note is that you'll probably want support for extensionless URLs like most other static site hosts. Azure and IIS don't support this by default, but you can configure it using the following web.config file:

        <rule name="html">
          <match url="(.*)" />
            <add input="{REQUEST_FILENAME}" matchType="IsFile" negate="true" />
            <add input="{REQUEST_FILENAME}" matchType="IsDirectory" negate="true" />
          <action type="Rewrite" url="{R:1}.html" />

You can either upload this file to your /site/wwwroot folder separately or place it in your Wyam input folder so it always gets copied to the output folder for upload. A more detailed examination of web.config files for static sites can be found at this blog post.

If you want to automate the upload process, you can consider using Kudu or read this blog post for an approach that uses FTP.