Basically, here are the few steps you've to do for it:
1. Open your Gmail. Click on Buzz in column on left side. Then once it has opened, there's a link called 'x connected sites' - in my case it is '5 Connected Sites' - it'll be different for everyone. So, you've to click that, a pop-up will open, you select your twitter page, and there you go. Now, every tweet will automatically be seen on Buzz.
2. Login to your Facebook. Search for Twitter. It'll open an application of twitter. Click on it, it'll ask you for your twitter's username/password credentials. Once done, click on a button 'Connect my Facebook with Twitter' sort of button on top. Once clicked, now your Facebook is also connected with Twitter.
This way, you can update your status on Twitter, Buzz and Facebook by just a new Tweet. For new tweets, download a Twitter desktop client. I used Snitter. Its very light, and looks nice.
Enjoy Tweeting, Buzzing, and Facebooking!