As I mentioned before there are two levels of users in my mind while writing this tutorial:

1. User A: who will carefully following instructions no matter how bad they are and can do thing even without knowing how they work or not worrying about potentially screwing thing up (like myself)
2. User B: who will screw up no matter how clear the instructions are

Users who fit the “B” criteria must get a friend who is more like user A to do it or hire a geek.

User A must check to ensure you have the following:

1. Access to both your WordPress install (admin username and password) and to your MySQL/phpAdmin (or at least your hosts Control Panel)
2. FTP client, a toll to move files from your computer hard drive to the server and vise versa

Steps below is provided with the assumption that you are familiar with the use of phpAdmin and FTP. Let us assume that your WordPress is installed at http://www.mywpsite.com/

On your site (Step A)

1. Log into your WP site using the admin login and password (http://www.mywpsite.com/wp-admin)
2. Make a list of all plugins that are active (newer version has deactivate all and activate all features)
3. Deactivate all active plugins

On the server (Step B)

1. Log into your phpAdmin using the login and password provided or set in your control panel to access this portion of the service (usually at http://mysql.mywpsite.com/)
2. Select the database where your WordPress is installed (f there are more than one DB)
3. Follow the visual instructions provided here to download all your WP database tables. Alternatively, you can use the WordPress Backup plugin this comes default (newer version have a XML import feature to download site data) with your old version of WordPress, but I find this technique easier and definitely a sure shot way to ensure you get all you valuable data backed up