You can download a Desktop client for Google Buzz (need Adobe AIR). You can read more and get the download link also here
Regarding browser extensions you can find Chrome and Firefox Extension details here on Ghacks.net. This page also includes two user scripts too.
Two userscripts are also available right now. Google Buzz Comment emoticons adds emoticon support to the comments and posts while Google Buzz Count Hide hides the unread status message count in Gmail
Firefox Add on details here