BioWare has just published a website update detailing its new Star Wars: The Old Republic character transfer service. Eligibility requirements are pretty straightforward: Your account can't be banned, and the character in question can't be a guildmaster.
BioWare says that guilds will not be transferred, so if you're a guild leader, you'll need to re-form on your new shard and petition customer service for access to your guild bank. The posting says that transfers will be made available gradually, starting with the least populated servers first. An updated listing of servers is also available. Further details, including how to start the transfer process, are available at the official SWTOR site.