Hap, a couple of things to do:
Go to your Account Management screen and click on the Summary tab. There should be a series of games listed under "Your Game Accounts" near the center of the page. The one for the Beta looks like this:
I say all that because this is the official place where Blizzard will display an authentic "invitation" to the Beta. There are all sorts of folks sending out fake e-mails telling you to click on this or that link to accept an invitation to the Beta. They are phishing for your account in order to hack it. Steer clear.
Once you've confirmed this, click on the link in the image above (which is the game title in blue). This will take you to a page with the following:
There are two things you must do from this page. The first is to download the game client for your type of OS using a link in the bottom right corner. Second, you need to click the link above that titled PTR Character Copy. That link will take you through the steps to copy one or more of your toons from live servers to the beta server. I would recommend the destination of the Lost Isles server. This is the one I have my toons on atm. After the download you should have an additional launch icon on your desktop or in your menu or both.
If you have done all the above and still can't get in, I would suggest contacting Blizzard for help with the install and setup. They will probably want to document any issues with install, etc.