Credits : Contents of this post are totally inspired by http://rootmyandroid.org/root-samsung-galaxy-mini-gt-s5570-froyo-gingerbread.html but it needed a little correction plus i wanted to provide abridged version of it. This tutorial tells about rooting the phone which already has gingerbread installed. For froyo , check the above link because i have not tried those steps).so here i go :
1. Backup important contents of your phone.
You can use Super Backup app for the purpose. This app keeps the backup on the sd card in a folder by the name "smscontactsbackup" and keeps it safe. You can also copy the backup to your Computer.
2. make sure that your phone is charged at least 90% so that it does not goes off in the middle of the rooting process. Also be sure that your computer is set off with the antivirus and firewalls, the cable with the specific drivers must be ready. Get USB Drivers for Samsung Galaxy Mini GT-S5570(Windows 7) (direct link). For windows 8 you can try http://forum.xda-developers.com/showthread.php?t=2038555.(I have not tried it on windows 8)
3. Set Debugging Mode on through Settings>Developers and then check the box.
4. Download the required files
download here. transfer this file to your SD card and do not keep this in any folder but straight away in the SD card.
5. Turn off your phone and got to recovery mode by pressing the HOME+POWER BUTTON simultaneously.
6. Choose “Apply update from SD card”.
7. Use the volume rocker for navigation.
8. Choose the zip file you downloaded
9. wait for it to finish.
10. Your phone will automatically reboot. If not, reboot it yourself.
Done! now you have rooted your device.
Tried On : Samsung galaxy mini gt-s5570 aka tass with gingerbread
May work for : No other phone