The best way imho:
Backup the database using phpmyadmin
Backup your entire public_html folder
Read it again 100 times as people tend to "pass" this part...
Delete all your files except wp_content folder and wp_config.php (and maybe other custom files you might have like .htaccess and sitemaps)
Upload the latest wordpress version (don't upload wp_config.php and wp_config folder)
Upgrade all your wordpress plugins
Go to www.blablabla.xxx/wp-admin and upgrade the database