Though lot of people and online sites had been putting question marks on how Twitter is going to do what but it seems nobody is able to avoid it anyways. I see Twitter integrated in sites below the post, Twitter used for comment authentications and now Twitter gets into the Google Reader also.
It did not came as surprise to anybody who even is reading this because the way we all were seeing it every where and probably is the one network which an bring tons of traffic if you a have true followers.
In order to add Twitter button, you need to go to Google Reader settings and Send to Tab, then select the twitter icon. This will add the Twitter icon in Send to option which comes under every post. Netx things you should see is the popup blocker of the browser in case it is blocking.
However there is no Auth magic going on. It just pushes you to twitter site and then you need to login and tweet it.