When you're working with a WordPress Multisite, large or small, you will have to run some updates to the site at some point. Whether it's your WordPress version, a theme or a plugin, you'll want to make sure your site is up to date.
To start, most updates happen within the Network Admin dashboard. Once you're logged into the dashboard, you can see how many updates are needed for any given plugin/theme/WordPress core files.
You can run updates all at once in the 'Updates' page, or run updates at the plugin and theme level individually.
After clicking on the desired updates, you will be redirected to a page that will run through the update process. Once updates are done you will see "All done! Have fun!" which signifies the updates are complete.