So, you have activated your unlimited plan and want to use it? You just need to do as follows to disable / enable mobile data on Xperia Z and other Sony Xperia devices:
1. Open Settings application
2. Under Wireless & Networks tap "More"
3. Open Mobile Networks.
4. Mark "Mobile data traffic" to use the internet via your mobile network
** Note that to avoid extra charges, make sure Data Roaming is disabled. Otherwise you will be receiving data when roaming