Need some help installing recaptcha

hi there I'm using one of html5up.net templates I've managed to display the recaptcha widget, my dyslexic brain cant figure out the private key and how to create the rule to send a message only once the recaptcha has verified the user TIA Avi -- You received this message because you are subscribed to the Google Groups "reCAPTCHA" group. To unsubscribe from this group and stop receiving emails from it, send an email to recaptcha+unsubscribe@googlegroups.com. To post to this group, send email to recaptcha@googlegroups.com. Visit this group at http://bit.ly/1dkFnYd. For more options, visit http://bit.ly/P65DvS.