With which host are you? Does your host have a special file manager? Is there only FTP? Is there WebDAV?
In fact, there are many ways to install WordPress on a web server.
1) Installing through a script installer like Fantastico, Installatron or Softaculous
If there is this option in your web hosting, just install it through here and it will install painlessly, but this option isn’t everywhere.
2) Installing through your hosting’s file manager
You need to upload the file and unzip it in the “htdocs”, “www” or “public_html” folder. Usually there is an unzip function in file managers like Monsta or cPanel.
3) Installing through WebDAV (WebDisk for cPanel)
3.1) You need to connect to your server with your credentials and then you add the ZIP file. After finishing upload you will need to unzip it inside.
3.2) Unzip in a local folder and upload all files through a batch upload
4) Installing through FTP
Basically the same as WebDAV.