Great questions, and so great to see so many wordpress.com users (usually we just hear from Blogger and wordpress.org users!).
Currently we just have the "button" to link to your community, but we're working on a full-functioning "image" widget that will look like the other widgets and work in Wordpress.com blogs.
First, make sure you have created a community. Click the communities tab, and you should see a place that says "communities I own" on the left.
Next, when you click the "add a button to my blog", a window will pop up, make sure you choose "Link to: My Community."
If you have multiple communities you can select which community it should link to at the bottom of the page. Grab the code, in the box, and then paste it into a HTML widget.
Did it work now? I'm following this conversation, so I'll get updates!