When I visit the Settings page I get the following error:

warning: mkdir(files): Permission denied in /.../includes/file.inc on line 91.
The directory files does not exist. 

Drupal uses a single directory for the storage of various files (for example attachments to content). When you visit the settings page it will check if the file directory exists and tries to create it when it doesn't exist.

However if the webserver doesn't have write permission (and it shouldn't) in the directory where the file directory will be created you'll get an error. In order to fix this first think about the name of the directory you want to use. By default Drupal uses the name "files".

When you've decided on the name create a directory with that name in the Drupal base directory and give the world ("Other" in most programs) read, write and execute permissions.

If you decided to use a different name for the files directory change the value of "File system path" under "File system settings" on the settings page and press "Save configuration"