It's both automatic and manual. It syncs automatically whenever plugged into power and connected to wifi (and your computer is awake with iTunes open). You can also force it to sync any time from Settings>General>iTunes wifi sync, for which it doesn't need to be plugged into power.
The way to check if it's working is to connect your phone to iTunes via USB (which you need to do once anyway) and then disconnect it. If the phone disappears from iTunes' device list on the left, it's not set up for wifi sync. It should stay there in the list because it's still connected via wifi. If the device does disappear, hard reset the phone, that fixed it for me.
And yes make sure the wifi option is enabled in iTunes.