Before you root your phone you have to first of all know what rooting is all about.

Rooting is a process of unlocking the operating system of your phone in other to install some application not approved by the manufacturer of the operating system of your phone, update the operating system, replacing the firmware and also customizing the phone to your own taste or satisfaction.


Things to do before you start rooting:
1: Install a good Android Debug Bridge (ADB) driver on your device. Download the software from here
2: Enable unknown source since you are not rooting with a PC
3: Charge your Android phone battery properly
4: Enable USB debugging on your Android phone by doing it this way; Click on settings on your phone=> Locate Applications=> Locate Development or Development Options=> Locate USB Debugging and then enable it and also enable the stay awake option to keep your phone from sleeping.
After you have already put all this in place now is to get you the software to get your job done.

Also check TIPS TO BOOST YOUR ANDRIOD WHEN IT IS SLOW

Here is a list of the seven (7) software to get you started.
1: How To Root: This awesome application software help with a rooting guide for android phone. It has an amazing features like detecting the phone brand, model and phone version automatically, it also include a tool that will notify you if your android device was rooted correctly. This wonderful software can be used on PC to root phone.
To use this software, download it and select your device from its database and follow the rooting methods to get yours done.
This tool can be downloaded here

2: VRoot: This is another wonderful tool that enables you to root your android device with ease. It supports most greatly with older version of android and it gives you an edge compared to some apps that enable rooting only for android devices. This tool can root/unroot devices running on Android 2.2 to the latest operating system.
This app can be downloaded here

3: Framaroot: This is one of the most used and popular rooting application and since its existence it have recorded a wide range of success. This app also let you root your android device without using a PC. What you just need to do is to download and install it, after that launch the app and then root your device choosing from a list of available exploits. Gionee, Techno and most MTK device will normally use the barahir exploit.
This app can be downloaded from here.

4: Z4root: This is one of the rooting device used in mobile phones. One of its advantage is that it can be used to root both old and new android devices.
You can download it here

5: Universal AndRoot: This is one of the easiest app to use. Just download it, install it and lauch it and then click on root and your device will be rooted successfully. It is very easy and you can also use this device to unroot your android phone if you wish to unroot it back.
Download the app here

6: Root Master: This app also serves as a very good alternative rooting app that can help you root your phone.
Download the app here

7: Easy Rooting Toolkit: Just as it is so does the name apply. It is very easy to use for phone rooting without using a PC.
Download the app here

Note: Rooting with a PC requires little knowledge but with this entire app above you can root your android device easily and it can be done by you.
- See more at: http://www.techskulz.com/2014/11/top-seven-7-free-software-apps-that.html#sthash.DLG6PqAM.dpuf