This tutorial will take you step by step how to backup your Joomla 2.5 installation using Akeeba Backup.
Download Akeeba Backup
Download Akeeba backup from here.
Install Akeeba Backup
Extensions >> Extension Manager
Browse >> com_akeeba >> Upload & Install
Components >> Akeeba Backup
The general settings are fine and there is no need for any modification unless you are trying to do something more advanced.
Fill in information appropriately. Then Backup Now!
Patiently wait for completion. Do not exit this screen until finished.