I own a Sony Tablet S and recently I noticed that some times the screen turns on witout me even touching it.It behaves like a random thing, altough It is problably not.
Mine started doing the same thing, I think it was checking for updates. When I turned off my WiFi, it stopped. I got a free airplane app and now, before I turn the tablet off, I tap the app to turn off the wireless. Best part is, my battery lasts a lot longer now.
The app you're looking for is called Auto Airplane Mode (by DON) It does a fantastic job of automatically disabling the WiFi when the screen blanks, which, as Spider points out, does wonders for battery life. However, if that doesn't do it I have another suggestion but try that first. There is another Airplane app on the Store but it's a fail.
You don't need to change any settings on the app unless it needs to be set to run on boot.