If you are experiencing the "insufficient storage available" problem then you are probable eager to find a solution so we will get right to it.

BE AWARE: ROOTING your android phone will void the warranty on your device.

First download framaroot from here or use the qr code from: http://forum.xda-developers.com/showthread.php?t=2130276
You can also check to see if your phone is in the compatibility list on the same page. The folloing phones are definitely on the list:

Samsung Galaxy S GT-i9000
Samsung Galaxy S2 AT&T SGH-I777
Samsung Galaxy S2 Epic 4G Touch - SPH-D710
Samsung Galaxy S2 GT-I9100
Samsung Galaxy S3 GT-I9300
Samsung Galaxy S3 LTE GT-I9305

Download the Framaroot .apk file.
If your android phone is on the list then select a .apk file to download from the list of attached files. The latest available version should work for you. Click to download the file or go to the page from your computer, click on the QR code link then use your phones QR reader to download the file.

Pull down the notification bar on your phone and press the completed download notification to let it install on your device.
If you lose the file or the notification from the notification area before installing, you can find it using your "My Files" app. Browse to: All Files --> sdcard0 --> Download

Your Download folder might be the extSdCard if you have personally moved it to that location previously.

Install the Framaroot apk file.
Your phone might inform you that the installation has been blocked for your security and will not install programs that don't come from Google Play. If this message comes up, click on the settings button, then scroll down to the line that says " Unknown sources" and place a check in the box next to it. You can always come back here and uncheck it after you have finished fixing your phone.

When it opens up after installing, select Superusersu, Aragorn, and then install.

It will ask you to reboot your device. Do so.

When your device has rebooted then go back to the Google Play store and search for "Terminal emulator".
You can install the free Android Treminal emulator by Jack Palevich or any other terminal emulator of your choice.

Open the terminal emulator and at the $ prompt, type:

su

-then press enter. Grant the emulator super user access.

- The $ prompt will now be a # prompt. Type the following ( the # in the following commands will already be present at the begining of each line) and press enter after each command.

#cd /
#cd /data/log/
#pwd

- the pwd stands for Present Working Directory. We do this command to MAKE SURE you are in the right folder otherwise you will delete files that you did not intend to. You do this at your own risk. We accept no responsibility for data loss that renders your phone unusable.
After issuing the pwd command your should see something similar to the following:

/data/log
root@android: /data/log #

Please note that the next linux command will delete ALL the files within the directory you are in , which should be the /data/log directory.
If you are sure you are in the right directory then type the following command:

# rm *

Your log folder should now be empty.
You can type:

# exit
$ exit

These exit commands will first take you out of super user mode then close the terminal emulator.

Go and check your storage space to see how much space has been cleared. 

Congratulations! you should no longer be seeing the "insufficient storage available" error message.

Don't forget to go back to your phone Settings --> Security --> Unknown Sources , and remove the check from the checkbox.