Continental no longer offers a free standby option in the traditional sense (show up at the airport, ask, and hope that a seat is still empty when they are ready to close the door). Instead they have switched to a "Same Day Confirmed" (SDC) plan whereby your change request is confirmed in exchange for a fee in the majority of cases. So, how does it work?
You must be within 24 hours of your scheduled departure time.
You must be wthin 12 hours of the desired new departure time.
There must be seats available in the same fare bucket (the actual fare bucket, not just the booked cabin) at the time of the request. If there aer no seats available you can be listed as a standby and cleared at the gate. This still requires paying the fee. If you do not clear you are not charged.
You must pay the SDC fee. This fee is $50 for everyone except Platinum Elites; they pay $25.