You will have to wait until they announce the beta and see then how to enter it. I have read that the soonest they will be announcing the beta will be in August. In the meantime you can check out the site I have listed below they are keeping up with the beta launch.
How does the Diablo 3 beta selection process work?
There is no surefire way to increase your chances. The purpose of the beta for Diablo 3, at least at first is to test the stability of the servers and to determine what systems are capable of running the game. They just updated the system check software on the beta opt-in page, so it would benefit to re-check your system specs. Fan sites also have contests for beta-keys, so if you don't get selected in one of the first few waves of beta invites, you can always try that route.
Beta for Diablo 3 just went under way some time around Tuesday Sept. 20th, only a handful, probably less than 100 beta keys have gone out at this point. A majority of people who get to play did not receive a beta key and just had their battle.net accounts activated for the beta test. so if anyone is willing to let you play would have to give you full access to their account, including all games that are linked to it, so the likely hood some one will do that is very slim. Luckily their is still plenty of time for blizzard to choose you, or try to win a beta key before the beta is over. Best of luck.
P.S. if you receive an E-mail saying you've been invited to the Diablo 3 beta, do not follow any links on that E-mail, go strait to battle.net to see if your account has been activated by blizzard, there are a lot of phishing e-mails going out already trying to steal your battle.net account.
Has anybody got the Diablo 3 beta test account here? I want to play a little?
If you are looking to play a little, then you need to try the D3 sandbox. Don't pay anything, or download the Beta, you can't get in to the beta without a beta key.
The following link is what the D3 sandbox does, and how to play it. Very cool.