Installing themes is pretty easy, and consists of two parts:

1. Unzip the downloaded archive and upload the enclosed folder into your themes directory. On a normal installation, DIR_THE is set to themes, which means you should upload the directory you unzipped into the themes directory of the base location Theia is installed in.
2. Install the theme in Theia; on the "theme statistics" page (admin tool 102), you should the name of the theme appear in the list of themes, and the status should read "not installed"; click the accompanied "install theme" link to install the theme. This adds the record into Theia's database, and allows the theme to be used.

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Things to consider

Sometimes themes will need to be enabled after installing them. To enable or disable a theme, use the "enable / disable theme" link on tools (admin tool 187).

The theme's directory, and associated files, only need to be "writable" when you wish to customize this theme's CSS, templates or images using Theia's interface. Being "writable" means the web server has permission to write to the directory and it's accompanied files. On most systems this means changing the directory and file permission to chmod 0777. Similarly, if you are on a dedicated server, you can just chown the files to the user that the web server runs as.