According to a press release put out today, Star Trek Online will hold its open beta from January 12th through January 26th. There are some preorder deals that will give you an open beta key, and there are bound to be numerous opportunities to win one at various spots around the net.
Star Trek Online is currently in closed beta, which began last month. Champions Online six-month and lifetime subscribers have been told that they'll be in the closed beta before the end of the year, so those folks should get at least a month of beta access before the game hits the retail shelves on February 2nd, 2010.
Once the open beta begins, you'll likely see a flood of information and guides about STO since the NDA will have been lifted. This will provide everyone with key information as to the finer details of the gameplay mechanics.