This viral Twitter prank uses a pretty standard trick to get you to post something to Twitter, using no JavaScript and only a very little bit of CSS. It requires only that you're first logged in to twitter.com (and that your browser's fonts are pretty close to standard so that things line up correctly).
The attack page creates a button labeled "Don't Click" that does nothing at all, but it also loads twitter.com in an <IFRAME> directly on top of the button. That IFRAME is then made completely transparent using CSS.
When you click the button, you're actually clicking on the (now invisible) 'Update' button on Twitter's web interface instead; assuming you're logged in to Twitter, you'll immediately post whatever's in the form input box. Thanks to Twitter's ?status= URL feature (that allows Twitter to be pre-loaded with a message), it's very easy for the attacker to drop the following message in:
Don't Click: http://tinyurl.com/amgzs6
That TinyURL expands to http://www.umoor.eu/blog/yes-we-can.php, the attack page; in this way your followers are also enticed to propagate the "attack" (which has proven quite successful).
No accounts were compromised by this prank; you don't need to change your Twitter password. For more information, check out the source to this page, which includes the attack (but makes the Twitter IFRAME partially visible so you can see it; it also puts another <DIV> on top of it to protect you from accidentally clicking the "Submit" button).
See also: an explanation (en Français) by the author of this attack, originally launched in January 2009.
Update: as of 1:40PM EST, twitter.com is using some JavaScript to try to detect when it's being loaded in an IFRAME:
if (window.top !== window.self) { window.top.location.href = window.self.location.href; }
If you try to load Twitter in an IFRAME you'll find the browser redirected to Twitter automatically (in this case, you'll never have an opportunity to click on "Don't Click"). I've therefore removed the attack from this page, but you can still see it if you view source.
—Daniel Sandler (@dsandler), 12 February 2009