Once you've installed the plugin, go to Settings - BibSonomy and at least enter your username and API key. Then test your setup with a click on Show posts, select a post and submit it with a click on Post selection - your post will appear as a new bookmark on BibSonomy.
While it's a really nice thing to have your blog posts synchronized with BibSonomy another powerful feature is to integrate your bookmarks, publications or tags into your content. Publishing your tag cloud from BibSonomy boils down to this simple shortcode: [bibsonomy-tags]. More complex requests like retrieving the three most recent publications that are tagged with folksonomy is possible too: [bibsonomy-posts resourceType="bibtex" tags="folksonomy" end="3"]. Have a look at more examples.