You need to apply via this page.
(Note: the user who wants to be verified needs to be logged in to Twitter before completing that application form.)
We’re starting with well-known accounts that have had problems with impersonation or identity confusion. (For example, well-known artists, athletes, actors, public officials, and public agencies). We may verify more accounts in the future, but because of the cost and time required, we’re only testing this feature with a small set of folks for the time being. As the test progresses we may be able to expand this test to more accounts over the next several months.
This is all still in beta, and it’s worth noting that your odds of being verified aren’t exactly high. I know of several well-known, high-profile Twitter celebrities whose applications were completely ignored.
Also note that once verified, if you change your profile information your account will become unverified, and you’ll lose the badge and have to re-apply. I wonder which genius created that template.
Still, the perks are enormous. Free coffee, unlimited tweets per month, and 24/7 access to Biz Stone via your own personal Twitter mobile phone. Allegedly.