I have just upgraded my WordPress sites to the latest WordPress version which is 2.6. The process is fairly simple. Following is a summary of the steps for upgrading. For a more detailed version, please refer to the WordPress Codex site.

1. The first thing to do is to back up your existing WordPress site in case something goes wrong! Check out my earlier blog on WordPress Database Backup below for details.
2. Next get the latest WordPress zip file and download it to you computer. Extract the files after downloading it.
3. Connect to your site using a FTP program.
4. Delete your old wp-includes and wp-admin directories.
5. Take care to preserve your old wp-config.php file in the root directory! Do not delete it. This file contains current settings for your existing installation eg database sign-in information. Compare your existing file with the new installation file wp-config-sample.php. Copy your settings (// ** MySQL settings ** //) to the sample file and rename it to wp-config.php. This is the new wp-config.php file you should upload.
6. Copy the CONTENTS of the new wp-content folder (including the contents of the plugins and themes sub-folders) to the old directories. DO NOT copy the entire folder or sub-folders as this will overwrite all your customizations and added content!
7. Copy all other WordPress files to your server, overwriting old files in the root directory.
8. Login to your WordPress admin page at www.your-domain-name.com/wp-admin. You will be asked to login again. If a database upgrade is necessary, WordPress will automatically detect it and you will be asked to upgrade the database. Click on the link provided and follow the instructions and your database will be upgraded to be compatible to the latest version of WordPress.
9. Clear your cache if you have enabled caching so that your changes will appear to users more immediately.

Your WordPress installation is now successfully upgraded!