Google Sites lets you create public or internal web sites, while Google Apps Scripts can save time by sending emails, scheduling calendar events and more with one click -- now Google've enabled scripts to support multi-step workflows in sites. "You can create, edit, and launch Google Apps Scripts from any Google Site, which allows you to automate business processes that involve multiple apps.
For e.g., you can create a site to browse and sign up for training sessions. On a training site, you could've a "Register Now" button on each classes page that would automatically add users to class roster, add the class to their Calendar, and email them to confirm enrollment," explained Google.
You can build a script by clicking "More actions" > "Manage site" > "Apps Scripts." Once you've added a script to your site, you can add links or buttons to trigger script from any page.
More Info: Google Apps Script site