There are different ways to open a door. By shooting, by approaching and of course by pressing a button. I built a small box around a brush which uses a texture out of the base_button category.
Select the placeholder, press the right mouse button, go to func and then click on func_button. You've just created your first button (blue lines).
Leave the button selected and open the entity window:
The button can only be connected to entities, whatever they may fulfill. You could connect it to a target_delay (that's another tutorial) or to a door so it opens. That's what we will do now. First deselect everything. Now select the button, then the door and press Ctrl+k. Do this with the other part of the door, too. You should see two blue lines with arrows now, directing from the button to the doors.
You should copy the button and place it in the other room, too, so you can also go back. But don't forget to change the "angle" value then. Here it would be possible to delete the "health" key so you can try out both settings.Here you can get the maps for this tutorial (place them into baseq3/maps):