I have been trying to get Facebook Connect working on WebOS and having no luck of googling the answer, so I've decided to build it myself.
Below are the steps you need to get it working
Create a facebook app at http://www.facebook.com/developers/createapp.php
Setting up the website to your domain, in my case would be www.paschar.com, but you need to set it to anything that suites you
Create your callback url on your website, which can be any url, in my case it's www.paschar.com/webos/callback. Set it automatically redirect to following authorizing url upon receiving "code" in the QueryString
https://graph.facebook.com/oauth/access_token?client_id=[your clientid]&redirect_uri=[your redirect url, i use the same one]&client_secret=[your client secret]&code=[the code you receive form querystring]
Now that everything you need outside of WebOS is done, you can download my "facebook webos sdk" from https://github.com/Nyceane/facebook-webos-sdk make sure you change the link to your own callback url in fbconnectassistant.js.
You should be able to see following screens step by step when successful.
If you find this helpful please feel free to make any comments or give donation. I am trying to raise $7,500 to attend TED2012 Conference.