Installing Kirby couldn't be simpler. Just connect to your FTP-Server and upload all files contained in the Kirby package to the document root of your server – done!
Visit http://yourdomain.com (you should probably replace the with your url :)) and take a look at your brand new, Kirby-flavoured site.
Mac users can find a tutorial about how to run Kirby on MAMP in the blog.
There's also a great article by Sascha Lack about how to install Kirby on XAMPP (german)
I've installed a little demo theme, so you will hopefully find it easier to take your first baby-steps with Kirby. If you like to have a fresh install without the template and demo content just let me know. bastian@getkirby.com

If you want to run Kirby in a subfolder like http://yourdomain.com/subfolder you need to make some simple adjustments first. Go to site/config/config.php and make sure you manually set the url config variable:
c::set('url', 'http://yourdomain.com/subfolder');
Afterwards make sure to also set the subfolder name:
c::set('subfolder', 'subfolder');
You probably also need to adjust the RewriteBase in the .htaccess file if you want to use mod_rewrite.
RewriteBase /subfolder
If you are not allowed to have your own .htaccess file or to use mod_rewrite, go to site/config/config.php and search for the part where you can switch off url rewriting.
c::set('rewrite', false);
You also need to manually set the url for your site then…
c::set('url', 'http://yourdomain.com');