How to Root your Android Phone (without PC)

The easiest way is to use KingoRoot, it literally performs the root process with just one tap.

The only complicated part is actually getting that app onto your Android device. That's because it's not available in the Google Play Store; instead, you must download the KingoRoot APK and manually install it.

Device powered on.
At least 50% battery level.
Internet connection necessary (Wi-Fi network suggested).
Allow installation of apps from unknown sources.
 Settings > Security > Unknown Sources  

1. First download the KingoRoot app from any of the following sites:
Official: http://adf.ly/1fWAV5
4shared: http://adf.ly/1fX2hO
MediaFire: http://adf.ly/1fhfZP

2. Install the download apk. Make sure Unknown Sources is enabled(checked). If you didn't check "Unknown Sources" in Settings > Security, then during installation, you will get a prompt "Install blocked", stating that "For security, your phone is set to block installation of apps obtained from unknown sources".

3. Launch KingoRoot. Kingo Root is very user-friendly and easy to use. Click "One Click Root" to start the rooting process.

That's it. Your Android device is now rooted. :)