Contact forms are not built into the theme (for many reasons) so we recommend using a 3rd party plugin for this. The free one we like is Contact Form 7 and the premium one we like is Gravity Forms both can be used to add forms anywhere on your site! We won’t support the plugins, but they are the ones we recommend.
Re-creating the demo contact page
For the live demo we simply used the recommended Symple Shortcodes plugin to insert a google map at the top of the site and then used the Contact Form 7 plugin to add the form below it, pretty simple stuff!