Upgrading from News Manager 3.0 to 3.1 should not have any problem - just copy/upload the whole plugin (news_manager.php and news_manager folder with its contents, overwriting all files) over your current installation.
There are, however, a few changes you should know before upgrading:
Tag pages are now included in the Sitemap by default. If you don't want this to happen, enable NMSITEMAPEXCLUDETAGS in gsconfig.php
Tag pages now have the tag name inserted in the <title> tag (for better SEO, like single post pages). If for whatever reason you want to avoid this, enter tag titleTag 0 in Custom Settings.
The older/newer page navigation now uses <span> instead of <div> for the "older posts" and "newer posts" elements. If this change is an issue for your site, enter markupNavItem div in Custom Settings.