First you need to update your system using update manager, Once your system is up to date you will be notified that “Ubuntu 13.04 is now available (you have 12.10).
If the Upgrade option is not shown then troubleshoot it. Open the Software Updater and click on the settings, now move to updates tab and check whether Notify me option is set to for any new version. If not, set it and close.
If you did not get the upgrade option even after the updates and troubleshooting, then run the below commands one by one in Terminal (Ctrl+Alt+t).
sudo apt-get update && sudo apt-get dist-upgrade
Issue the password for the user, when prompted.
sudo update-manager -c -d
The above command will give you the upgrade option, skip the below command if it works and continue with screen shots else you have to upgarde Ubuntu commandline using the below command.
sudo do-release-upgrade -d
Once you got the upgrade option on Software Updater, Click on the Upgrade. Issue the password to Authenticate it.
Next window will come up with Release Notes, Click Upgrade.
Final pop up window is for confirmation, Click Start Upgrade.
That’s it, once download complete it will automatically upgrade to Ubuntu 13.04. Check the do list after upgrading.
Hope this will be helpful for you!!!