Those don't exist yet, but will in a few hours. I met with the Facebook executive in charge on online marketing and he mentioned that in the next few days you will be able to check the homepage of facebook.com for a message on this. Check each morning, as that's when they post marketing messages.
You won't be able to get a first name, since Facebook employees have first dibs-- thus, Facebook.com/austin is probably not possible unless there is not an Austin at Facebook. So if you see this open up, let your colleagues know and start grabbing the urls for your own clients and sites that you own. For example, we might want to grab facebook.com/ringtones or facebook.com/weightloss. This is akin to the domain name registration rush.
For ones you can grab, make sure you first have a Facebook fan page, since you will be redirecting your old page (which will look like http://www.facebook.com/pages/AmazingMail/57424733160?ref=mf ) to facebook.com/amazingmail. I predict that these names are going to be worth a lot. Let's see if Facebook has procedures to prevent the name squatters and identity thieves from taking all the good names. Twitter had some of the same issues. Facebook is rapidly becoming the #2 search engine-- yes, they are a search engine, too-- at nearly a billion queries a month.
But don't wait-- get your pages built now, and then be ready to grab your vanity urls!
You can start getting theses tonight at 9PM PST, Friday, June 12 2009.
You can see the count down timer by going here http://facebook.com/username

Wilco on Jun 12, 2009 at 1:16pm
Too bad they restricted this to accounts that where made prior to this press release :-(
Dennis Yu on Jun 12, 2009 at 10:38pm
Wilco,
If you have a name brand, you can get an exception. Ping me if you need help.
zik on Jun 18, 2009 at 8:51am
need more info!