Can anyone point me in the direction of this tutorial?

It's literally one I/O connection. The control point has an output for when it is captured and the door has an input for when to open.

KeKo, you can control which team can open a door (which team can trigger the trigger_multiple) by setting the trigger_multiple's 'Filter Name' keyvalue to a Filter_activator_tfteam which would be set up for a specific team. You can make two of these team filters - one for each team: filter_red & filter_blue. You can then make two of the door-opener 'trigger_multiple's, name each one for each team, and set them to their corresponding team filters. Trigger_multiple has Enable & Disable inputs, so depending on which team owns the point, you can send outputs to Disable a specific team's door trigger & enable the opposite.

I'm not sure if there is an easier way, I think there is some easy 'associate these things with the owner of the point', but I haven't used them so I'm not sure.

An easier way would be pointing the filter that the door trigger uses to the control point itself, using the "Associated team entity" keyvalue. That way, when the point is captured, the door will instantly and automatically update so the new team that owns the point can open it.

If it's a closed off room, don't forget to teleport (or kill) players who might be trapped inside.

You don't even need the trigger for a door that just opens once. You can just open the door directly when the control point is captured.