I found this project that uses a GSM module (scroll down to see Picture 5). It seems the module has to be bought separately. I have old GSM cell phones lying around in the house. Shouldn't these phones contain such a chip? Is it possible to remove the chip and use it on a circuit board as shown in some of the pictures in the project?
Does connection cables exist for your phone ? Or, if it is a Nokia, are there pins behind the battery ?
If yes, your old phone is probably able to receive AT or FBUS command, allowing you to easily use the internal modem, for example to send/receive sms.
Search about this (for example on chiphacker), many people have done such things.
There also exists standalone GSM modules (example at SparkFun).
In cell phones, the RF components are very tightly integrated with everything else.
It may be possible to tap the interface between whatever local processor the phone uses, and the RF stage, but it would very likely not provide a simple interface similar to the module used on the linked page. In any event, it would be a significant challenge to even get access to the interface wiring, as most phones use PCBs with many layers (4-10), and all the parts are generally BGA.
Basically, there is a reason they sell phone modules like that.
@Klaus's idea about using the phone as a whole is a much better idea. No PCB hacking there.
If some nokia's have a built-in AT command interface, and you have one of those phones, you should be good to go. Effectively, the whole phone is one of those GSM modules.