Character transfers are going through final tests and will commence early next week. There will be an official announcement with all the details before they happen. The transfers won't be real-time, it can take about a day for the transfer to be finalized.
Some preliminary information in QA form with questions taken from the forums:
Q: Do quests start over?
A: No, you get to keep them
Q: Will we lose skill upgrades?
Q: Will the journal stats be reset?
Q: Are we going to be forced to rename our character?
A: Only if the exact name is already taken on the NA server
Q: Will you have to pay for a NA copy during or after the free month of transfers?
A: No, but there will be a transfer fee back and forth between EU and NA servers for those that want to transfer their characters.
Q: Can we change race?
Q: My EU account is unsubbed, can I still transfer?
Update to original post:
Q: Will I need to get an active subscription on NA1 to play?
A: Yes you have to buy a subscription package on NA1 (also see below)
Q: Can I transfer my remaining subscription on EU1 to NA1?
A: There are people that want to keep their EU account active so it's only by request if you file a customer support ticket AFTER the transfer is complete. You also need to buy a subscription on the NA1 server whether you transfer an active subscription on EU1 or not. The EU1 remaining subscription time is added to the subscription time you buy on NA1.