WordPress.org

1. Unzip the wp-contact-form-iii.zip file and upload the entire wp-contact-form-iii subdirectory to wp-content/plugins/
2. Log into your blog and activate the plugin
3. Go to Options -> Contact Form III to configure everything like email address and antispam question
4. Create a Page or a Post where you want the contact form to be and insert [contactform]

Upgrading

If you're are upgrading from 1.5.x to 1.6.x you need to:

1. Delete the old supdirectory "wp-contact-form-iii"
2. Upload the new.