Right now they're only verifying a handful of accounts, including well known accounts at risk of repeated, proven impersonation, and government agencies. they're only able to verify a small number of accounts now.
To verify your account
Log into the account you want to verify and fill this out. Make sure you're actively tweeting, your account is public, and your Twitter profile (name, bio, picture, website, etc.) is complete! Include the contact information of an agent/publicist/person that we can contact as an additional point of verification if necessary.
Linking to your Twitter profile from an official website is the fastest way to get verified. If an official website links back to your Twitter profile, send the link to the page. (A link to the exact page is best so we know where to find it!) Anything that will help them validate your will make things faster.