How can I build a GSM modem?

You can use a module like this:
http://www.alphamicro.net/components/line~line~12.asp
http://www.rfsolutions.co.uk/acatalog/GSM_Modems.html
http://www.gsm-modem.de/gsm-module.html
http://www.roundsolutions.com/gsm-modem/index.htm