1. Web Server Ownership
The first level is actually to make sure that your web server has ownership over the directories:
chown -R www-data:www-data your-wordpress-directory

2. Directory Permissions
The second level is also required – you must make sure that the directory permissions are properly set:
sudo find /var/www/wordpress/ -type d -exec chmod 755 {} \;
sudo find /var/www/wordpress/ -type f -exec chmod 644 {} \;

I’ve found that most solutions posted on the web show part two but skip the first part.