Other than build a good public transport network and use the policies to encourage them (and making them free if you can afford it), I'm not aware of ways to increase the usage.
For water and sewage, you always want to connect them directly to the grid and not through each other. So it should look like this:
https://steamcommunity.com/sharedfiles/filedetails/?id=2223944780
Connecting like this will cause problems:
https://steamcommunity.com/sharedfiles/filedetails/?id=2223945379