easiest way to detect a switch change using an arduino
@AndyAka's answer excellently describes a possible approach to addressing the requirement. 

This answer does not preclude the other one, but points to a single-IC pure solid-state  implementation of the same approach.

Use an AC-DC optocoupler with a logic level output, such as the Fairchild HCPL3700 or similar. I have selected the cheapest (for single units) such part from the Digikey database; just search for AC-DC optocouplers with logic level output, for alternatives:



The implementation for the specified requirement is provided in the datasheet:



The advantages of this solution are:


No discrete bridge rectifier or diodes required, rectification is internal
No mechanical relay, so less likelihood of device failure
Inexpensive: Entire solution including resistors and capacitors for under $4.50
Damping can be set up easily (see datasheet) to eliminate signal chattering
Output is designed specifically for TTL logic level
Less parts involved, less points of failure.
Available in SMD or through-hole DIP, choose whichever is preferable