How do I upgrade my Sony Xperia X10 mini to Android 2.1? I would like to explain to my friend who lives in another country how to upgrade their phone to Android 2.1 so that they can use WhatsApp.

How can they do this?
Try pointing them to this link on the Sony Mobile website: http://www.sonymobile.com/global-en/software/phones/xperia-x10-mini/

It has some software to download for mac or PC which will allow your friend to upgrade their device.