WordPress offers two main methods to install a plugin. One is WordPress' own baked-in Plugin Installer (results may vary) and the other is the manual method using SFTP or FTP. WordPress's automatic install makes life significantly easier, depending on your webhosting provider, however it might not be available for your hosting package. If this is the case, and your site doesn't support automatic install, you can still manually install plugins using FTP.

Honestly, if your host doesn't support automatic installation, you should seriously consider changing web hosts. The ability to automatically install WordPress updates, plugin updates, and new plugins is one of the reasons WordPress is great; the process is hard enough without letting things become outdated.