I have extracted and copied the source files from https://contao.org/de/download.html (Contao 4.1.2 zip) to my web space (givoo.de) per FTP.
After visiting the url givoo.de/web/install.php it tells me to set the password and directly after that I am getting this error:
Fatal error: Call to undefined function Patchwork\grapheme_strlen() in /kunden/484914_14059/webseiten/vendor/patchwork/utf8/src/Patchwork/Utf8.php on line 234
I mean, there is not much else to do. A composer or such is not needed with the newer versions beginning in 4.1 or so.
You need at least PHP 5.4 to run Contao 4. If you do run PHP 5.4 or higher already, then your PHP environment does not have the PHP intl extension enabled, which is currently required for Contao 4.
PHP intl is integrated into the PHP binary since PHP 5.4, however some Linux distributions come with a custom built PHP binary without the intl extension.
Check with your hosting provider if and how you can enable the PHP intl extension for your server.