The bookmarklet will:

Receive a short URL from the API

Open up your twitter homepage in a new tab (Firefox) or in a pop up with the short URL and the page title included in the textarea

(Or take you to the twitter login page, which will then redirect)Twitter Share Bookmarklet
To install just drag this link/button into your browser’s bookmarks toolbar:

Tweet This

For IE-Users: You will have to right-click on the link and choose Add to Favorites… After that, you will be warned, because it’s not a simple link, but a bookmarklet.  Choose Yes.