best servo/wireless adaptor for low power consumption

I want to build a few things with arduino that will use low power. Is there a way you can have arduino "wake on LAN" because I don't want it to constantly use power unless it is told to do so. afraid if wireless adaptor is added it will always be awake and draining power.

I basically want to patch into arduino via a web app or something and have it turn a nob when I give a command. it will be running on battery so I need it as energy efficient as possible.