The announcement briefly explains that testing phases will be conducted, in small focused groups from North America, then later expanding to other areas. Sorry, Aussies and Euros, you will have to wait. If you are selected, an email will come to the address you entered in your swtor.com profile. Although we have not heard it from an official source, we have been told by others who are currently testing that just because you were chosen to be a part of one testing group does not mean you will be a part of the next testing group. So jump on that email as soon as you get it.
If for some silly reason you have yet to sign up for testing, hop over to swtor.com now and do it right away!
[Minor Update: Bioware is calling these sessions Game Testing not beta testing. We have updated the article to reflect that.]