1. install samsung kies on your PC for so that you have the galaxy mini's drivers installed.
2. google for SuperOneClick v1.9.1 and download it (sorry i do not have sufficient post count to post links) [note that superoneclick will trigger some antivirus, but from my experience it is safe]
3. make sure your galaxy mini is in USB debugging mode
4. connect your galaxy mini to your pc via USB cable. Do not turn on USB storage on your phone. Just connect your USB cable and leave it.
5. Run SuperOneClick and click on the 'root' button. Respond to any pop up accordingly.
6. reboot your phone and it should be rooted, check your app drawer for the 'superuser' app to confirm (if it's there, it's rooted)
Disclaimer: I will not be responsible for anything that happens on your phone during the rooting process. Please do it at your own risk. You can google it to check that SuperOneClick does work on galaxy mini for many users already. I have personally rooted my mum's galaxy mini using SuperOneClick last week.
*after rooting you can install AdFree from the android market to block irritating ads on free apps, especially angry birds. It will make angry birds run more smoothly.