Yes and no. You don't pay for the Wifi, but you DO have to pay for the internet connection to come into the house. All Wifi signals have to originate from the internet, and those are almost always originated from a plugged in network connection. (The exception is the internet connection to your phone and a technology called tethering, but that's beyond the scope here.)
So, you have Internet -> Modem -> Wifi -> computer/tablet. You need to have the whole chain to browse the internet wirelessly.