I'm trying to get my arduino GSM shield working with the example "Send SMS" code provided. However, when I upload and compile the program, the serial monitor displays "SMS Messages Sender" and nothing else occurs.
I cannot leave a comment otherwise I wouldn't post this as an answer. There are several reasons why this could be happening. You need to provide a bit more info.
Are you powering the GSM shield properly or do you just have it plugged into the USB?
According to the Arduino GSM shield web page:
It is recommended that the board be powered with an external power supply that can provide between 700mA and 1000mA. Powering an Arduino and the GSM shield from a USB connection is not recommended, as USB cannot provide the required current for when the modem is in heavy use.
The modem can pull up to 2A of current at peak usage, which can occur during data transmission. This current is provided through the large orange capacitor on the board's surface.
Another thing to check is if your SIM card configured correctly. For example, does your SMS provider require a PIN to connect to the network?