Installing Joomla! on a remote server without Fantastico is quite similar to the localhost procedure. The method of creating a database varies greatly across hosting companies, and you are advised to contact the hosting company if there is any confusion as to how to go about doing this.
In order to install Joomla! on a non-Windows localhost, and for troubleshooting the installation, adequate documentation exists on the project website, at http://www.joomla.org, where an active forum exists with answers to virtually every problem that may be encountered during installation.