That depends on what you mean! You can use WiFi to connect to a wireless home network and that would be free (excluding the connection fee to your ISP that you pay anyway).
If you use WiFi to connect to any other networks (public hotspots), you may incur a charge. In the UK this would be payable in advance (normally by credit/debit card).
WiFi simply connects your device to a wireless network via some other piece of hardware (a router or access point). If you have access rights to the network, you will not be charged any more than you are at the moment barring any download limits.
On the other hand, if you use 3G technology to connect to the Internet or wap services (if the Tilt has such capability), it is highly likely that AT&T will charge for the service.