Can't get Recaptcha to Validate

In Joomla, I am setup a module with a PLAIN HTML Form as seen below.  I followed the 1st step for the client side integration by adding to my template file before /head. In my script I added 

.  The problem is I don't understand how to do step 2 for the server side integration.  Either the documentation isn't good enough or it's my lack of understanding.  But I sure could use some help if anyone has any advice.  The current setting will only show the recaptcha form but it does not validate.  

 (note this posts to a different website other than google to track the data.) First Name
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