Installing Nucleus is done through some steps:

1. Unzip

Unzip all files to a directory of your computer. Make sure the path names are used when unzipping. You should end up with the following directory structure (* stands for a number of files):

/*                           (main files for site)
/nucleus/*                   (main files for admin-area)
/nucleus/javascript/*        (javascript helper scripts)
/nucleus/libs/*              (Nucleus core libs)
/nucleus/language/*          (definitions of languages)
/nucleus/plugins/*           (plugin-dir)
/nucleus/xmlrpc/*            (XML-RPC interface)
/nucleus/documentation/*     (Documentation + admin-area help)
/nucleus/styles/*            (stylesheets for docs & admin-area)
/nucleus/forms/*             (skeletons for commentforms etc)
/extra/*                     (extra goodies, e.g. needed files to enable fancy URLs)
/skins/*                     (skins directory [imported skins will go here])
/media/*                     (media library directory [emtpy])

2. Upload files

Upload all files to your server, using your favorite FTP program. Make sure to upload .php files in ASCII mode! It might not work otherwise.

Optional:

1. To make your install process even easier, you can change the file permissions on config.php to 666. This way, the install script will be able to update it automatically instead of you having it to do manually. (Quick guide on how to change file permissions)
2. If you want to use file upload, you'll need to add write permissions to the /media/ directory. This is needed in order to allow PHP to write uploaded files into that directory. The directory should be chmodded to 777 (Quick guide on how to change file permissions). (If you have root access, you can instead chgrp the directory to the user that is running the httpd process (usually httpd or nobody, then chmod 775 the directory).
3. If you want to use the SkinFiles plugin to edit files, you'll need to change the permissions on all files and directories under the /skins/ directory. To be able to edit files, they should be chmodded to 666 (Quick guide on how to change file permissions). To be able to create new files or directories, the parent directory should be chmodded to 777.

3. Run install.php

Open your web browser open the URL below, where you adapt the yoursite and yourpath parts.

http://www.yoursite.com/yourpath/install.php

This install-script will prompt you for some information, and perform most of the installation for you. When everything has succeeded, install.php will provide you with further instructions. (you'll still need to delete some files manually)

4. Done!

You should now be able to visit your site at http://yoursite.com/yourpath/ (or whatever URL maps to the location where you uploaded the Nucleus site main files)