The easiest way to test the LCD and backpack is to connect to it to your computer and send data with a terminal program.
Use any mini-B USB cable to connect to the backpack. If you're using windows, you'll need to point it to an INF driver file. See below in the download section for that INF file. Mac and Linux do not require a driver.
After the backpack is plugged in, it will create a serial port. Under windows this is called a COM port. You can look in the Device Manager→Ports to see what the name of the COM port created is. You should see an entry appear/disappear when connecting the USB cable.
Now that the port is known, you can use your favorite terminal program to connect. For this example, we'll use the basic terminal built into Arduino. The only downside of the serial port monitor is that you can only send a full string at a time and there's a new line at the end. If you are using a more powerful monitor such as CoolTerm (mac) or RealTerm (Windows) you can watch as each character is entered
Start by selecting the same COM serial port that belongs to the backpack.