First, put down a logic_relay near your point so that you can find it. The logic_relay is optional but really helps keep your logic under control.
Next, name it something you can remember easily, for example i'll call mine "relay_capA"
Go to the logic_relay's "Outputs" tab and add a new output to open your door:
Lastly, go to the control point's "Outputs" tab and add an output to trigger the relay:
(Your cap point name, and the team who captures it, will obviously be different)
Alternately, you can bypass the logic_relay entirely and add an output to open the door directly from the capture point, but if you want your capture point to do multiple things then the logic_relay will help you keep them organized. Just think of it like a baton passing race.