The easiest way to connect to and control a Bartendro Dispenser is through your computer and an FTDI device. Something like this. Keep in mind that the Dispenser needs a 5V supply, but the UART signals should be 3.3V (the dispenser is 5V tolerant though). Then all you do is start a terminal program and connect to the appropriate serial port at 9600 baud 8,N,1. Type an exclamation point '!' at the prompt and your dispenser should respond with a message. Type 'help' and it should spit out a list of the commands you can use.
The LEDs will not work unless the Vin voltage (Dispenser pin 1) is greater than 12V. Also, by default, the numerous LED patterns won't work unless you provide a square wave with 2ms period to the SYNC signal (pin 7) on the dispenser.
If you decide to use an Arduino to send the SYNC signal and also want to send commands from your computer's command prompt through the Arduino, you'll need to use something like the SoftwareSerial library. This leaves the native UART of the Arduino as the computer interface, and allows you to set another set of pins (something like 10,11) as the software UART to communicate with the Dispenser.