How do we say when we try to use the tap in a kitchen or bathroom? Can I say "open the tap" or "turn on water"?
You can say turn on the tap or turn off the tap.
In this meaning, the word tap is mostly used in the UK. On the other hand, in the US, the word faucet is chiefly used.
You can say turn on the faucet or turn off the faucet.
The difference between the words tap and faucet has been talked here.