How to turn a wired dimmer into a wireless one?
I'm also an EE student. My senior project is similar to what you are doing. I would recommend:
1) choose a wireless standard. I used Bluetooth because it was part of the requirement. Good thing about bluetooth is its easy to use and has a relatively high bandwidth. Bad thing is that it is hard to broadcast your commands to multiple "slaves". Zigbee uses a mesh nextwork, and it allows you to do that, but Zigbee has a bandwidth restriction. 
2) choose a wireless module: look at microcontrollers with the wireless chips implemented. Put one on your arduino, and another one to the light. 
3) Program them. This requires you look up guides, read datasheets etc.