The plugin works in all major browsers (I've tried it in the latest version of Firefox) and installs on all of them automatically. After you've installed it, start a chat with someone and enable the new functionality from the Options menu at the bottom of the chat window. If you don't have it yet, you'll get it soon; Google is gradually rolling out the new feature to all users starting today.
This is obviously a big jab at Skype. With VoIP and video chat functionality in Gmail's familiar surroundings, many users will feel less need to ever use Skype. Sure, Skype's client has a ton more options than Gmail's simple video chat, but many users will prefer Gmail for precisely that reason. Google now needs to enable this functionality in Gtalk, and the circle will be complete; it'll be interesting to see what steps Skype will take to counter this threat.
See Google's video presentation of this new feature below.