As you demonstrated you would be best finding a module or add-on board that handles the SIM capabilities and integrates an antenna to receive GSM signals. As the above poster has included, the shield would be a relatively straightforward approach if you are set on using an Arduino.
As for websites that include numbers, it probably has a web interfaced hosted on a server that can send a command to an Arduino or similar microprocessor to check the status of a GSM module. A simple approach to this if you wanted to DIY would be a web server hosted on a Raspberry Pi since it is well documented like the Arduino.