First off, you'll need a Beta Early Access Code. There's now a couple of ways to get this, with the most obvious being to pre-purchase the game. Alternatively, you can grab one from one of various promos Activision Blizzard are running with other companies, such as KFC in the US.
A further promo has been set up with O2 and Virgin Media. Customers of those ISPs in the UK can now nab themselves an early access beta code via the Priority app.