But @balin did not mention being concernec about him being spied on. Like @Stefan mentions: Flightmode is exactly what @balin describes (especially since he put “hardware toggle” in parentheses). For Fairphone 1 (and other dual-SIM phones I know) you can also deactivate each of the SIM-slots separately in software.
If you want to hide your phone from any spy, you can put it in a Faraday’s pouch. Have a look at http://killyourphone.com/. I’ve sewed such a pouch using this shielding fabric and it works remarkably well.