How do I get news to show in the News widget?

By default, the News widget on a Guild Launch site shows any and all Announcements made in the 'News' forum of your site.  You can change this on the configuration menu of the site (details can be found here!)

To get a post to display in the widget, all you need to do is post it as an announcement in that forum.  There's a toggle when making the new post that will make it an announcement, which looks like this:

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