What do I need to do and how to use my iPhone while living in Mexico?
What I can tell you for sure is that you need to jailbreak, and then unlock your phone. To do so, perform the following:
Go to www.blackra1n.com
and download either the Mac or PC file. Once you have the file downloaded, hook your phone up to your pc, close iTunes, and then double click the blackra1n icon on your desktop. Once the blackra1n application window launches, click 'make it ra1n'. The phone will then be jailbroken, and reboot. Once your phone has rebooted, click on the blackra1n icon on your phone, and choose sn0w. Clicking on sn0w will unlock your phone. At this point, your phone is now unlocked, and can be used with any GSM carrier (i.e. any carrier that uses a sim card). Once you are in Mexico, sign up with a carrier down there, and put their sim card in your phone, reset your phone's network settings by going to Settings>General>Rest>Reset Network Settings. Your phone's network settings will reset, and you should now be able to use your iPhone with the Mexican carrier. I hope this helps. If you want to mess with themes and the like on your phone, go back to your blackra1n icon on your phone, and download Cydia and Rock. There are tons of forum posts dealing with these repository programs I am sure. If you have any further questions regarding using either, I am sure the community here on the forums will be more than happy to answer them. Cheers!