If you are new to working with Arduino a good place to start is here http://arduino.cc/en/Guide/HomePage
This is meant to be a collection of simple Arduino examples to help our customers get started. Code is tested on our Arduino Ethernet modules http://www.andymark.com/product-p/am-2287.htm Individual examples will be subfolders in this repository.
Go to http://files.andymark.com/AndyMark_AM-2640_LED_setup.pdf for some simple hookup instructions.
Make sure you connect the ground from the LED strip to the Arduino ground.
Communications to the LEDs requires a common ground to work.
NOTE: Make sure you do not apply much more than 5V to these LED strips or you could destroy them!
Handling note: Don't mess with the wiring while the power is on. This can cause voltage spikes
or sneak ground paths that can damage the LED strip!
Arduino info on how to install software libraries http://arduino.cc/en/Guide/Libraries
If you are new to Arduino there is a nice new training resource provided by a 3rd party here: http://www.arduinoclassroom.com/index.php/arduino-101