I found this method while travelling around Portugal (most beaches have wifi, but I don't usually carry a pc together with my surf board).
It is one of the simplest to root most android devices in a very safe and easy manner without actually using a computer.
- download Framaroot
- place it in your SD card or your cloud storage accessible from your mobile (ie dropbox)
- Install Framaroot.apk by tapping it
- try what exploit is for you, it won't hurt your phone.
Wait for the success prompt then reboot your device.
Check if you are successfully rooted by downloading and installing root check app from Play Store.
hope this is helpful