An adition to yrajabi's anwser:
In Android, AFAIK, when you connect to an active Wi-Fi network, mobile data (GPRS, 3G, etc) will be disabled (even if are turned on) temporary. So it would be OK to just connect to the Wi-Fi network. But, if you want to be sure about disabling mobile data, you should go to Settings -> Wi-Fi and Networks -> Mobile Data and uncheck the option to disable mobile data. (in ICS it's in Settings -> Wireless and Networks -> More -> Mobile Networks)
Sleep might change this if wifi is set to sleep when screen is off - wifi turns off and data comes back on(unless data is force-disabled as per yrajabi). To keep wifi on during sleep be sure to set: Settings> Wireless & Networks> Wi-Fi settings> MENU button> Advanced> Wifi Sleep policy to Never.