How do you open doors on FTL for iPad?

Solution 1:

To open doors, just tap the door subsystem; the game will auto-pause (by default) and you'll be able to toggle the doors by either tapping them, or dragging your finger over multiple doors.

Then just click it.

Solution 2:

You have to click on the Door Subsystem in order to enter "door mode" and open/close the doors. You will have a "Close all" and "Open all" buttons.

You could drag along the path to toggle the state of the doors. It is explained on the Tutorial. So once Door Subsystem selected you can drag your finger along the closed doors you want to open (for example).