Google Reader synchronization enables FeedDemon to access your Google Reader shared items, including the ability to share articles directly from FeedDemon's newspaper. If you're not familiar with Google Reader shared items, this help page on Google's site provides a nice overview.
To share an item, simply click the share icon that appears by that article.
You can also share articles in web pages that you're viewing in FeedDemon's tabbed browser - simply drag the browser tab to your shared items, or drag a hyperlink from the page you're viewing. You can even drag hyperlinks from your external browser into your shared items.