Considering that a LED strip power supply usually provides a bit more than nominal 12 volts (something like 12.3 in fact), you may be tempted to avoid connecting it to Arduino.
Most Arduinos have a Vin pin that can be connected to bigger voltages, with 9 volts recommended and 12 volts a safe maximum that, according to some, should be generally avoided. LED strip is usually run off 12 volts, Arduino works on 5 volts.
Before we start connecting the Arduino to a LED strip, let’s deal with the power source.