Just go into the admin part of joomla Components -> Contacts -> Contacts and create a new one. Next simply add a new menu item on the main and choose its lading page as single contact. This will make all the fields appear and you'll get an e-mail everytime someone fills out the form.
Now for the next problem, how to make it look like they did? As Shakespeare said, this is the question (and I am still trying to figure this out myself!)