Thank you for the kind comment and the feedback!
A floodgate can only be opened if the player stands on the floodgate tile and has 4 cards of the required tool type.
So for example to open the floodgate with the hammer icon, you need to stand on that tile while having (at least) 4 hammer cards in your deck. Only if these 2 conditions are fulfilled the button will appear and you will be able to open the floodgate.
I hope it helps!