Go to: https://www.google.com/recaptcha/admin/ Create a new re-captcha. Specify the domains where the captcha will be used.
Get the site key and the secret key.
In the form.html code, search for
<div class="g-recaptcha" data-sitekey="xxxxxxxxxxx"></div>paste the site key in the data-sitekey attribute
Open handler.php and search for initSecretKey copy your secret key to initSecretKey function.
Make more customizations in the handler.php file (your email address, "From" address etc )
Upload and test the form