For use this plugin with send e-mail form (for example - "feedback" or "contact us" form on your site for anonymous users), you need to create view with form with some of next field (field "Body" is required):

This sample view for send "contact us" form: (online-demo sample)

<div class="common-form">
  
<h5 class="title">
       Contact us
</h5>
   @
if (ViewData["ReCaptchaFormResult"] == "Mail was sent")
   {
      
<p style="color: green;">
          
<strong>Thank you for feedback! Your message was save.</strong></p>
   }
  
<form method="post" action="">
   @Html.AntiForgeryToken()
  
<!-- this contact form will send an email to the email address defined in system/settings/smtp-->
   @*
<input type="hidden" name="RedirectUrl" value='@Url.FrontUrl().PageUrl("Thankyou")'/>*@
  
<input type="hidden" name="recaptcha_form_action" value='SENDEMAIL' /><!-- SENDEMAIL or ADDCONTENT -->
  
<table>
      
<tbody>
           @*
<tr>
               <th>
                   <label for="from">
                       From email:</label>
               </th>
               <td>
                   <input type="text" id="from" name="From" data-val-required="From is required" data-val="true"
                     data-val-regex-pattern = "\b[a-zA-Z0-9._%\-+']+@@[a-zA-Z0-9._\-]+\.[a-zA-Z]{2,6}\b"
                     data-val-regex = "Not valid e-mail." />
                   @Html.ValidationMessageForInput("From")
               </td>
           </tr>
           <tr>
               <th>
                   <label for="subject">
                       Subject:</label>
               </th>
               <td>
                   <input type="text" id="subject" name="Subject" />
               </td>
           </tr>
*@
          
<tr>
              
<th>
                  
<label for="body">
                       Body:
</label>
              
</th>
              
<td>
                  
<textarea id="body" name="Body" cols="20" rows="10" data-val-required="Body is required"
                      
data-val="true"></textarea>
                   @Html.ValidationMessageForInput(
"Body")
              
</td>
          
</tr>
          
<tr>
              
<th>
                  
<label for="contact_name">
                       Contact name:
</label>
              
</th>
              
<td>
                  
<input type="text" id="contact_name" name="contact_name" />
              
</td>
          
</tr>
          
<tr>
              
<th>
                  
<label for="contact_email">
                       Contact e-mail:
</label>
              
</th>
              
<td>
                  
<input type="text" id="contact_email" name="contact_email" />
              
</td>
          
</tr>
          
<tr>
              
<th>
                  
<label for="contact_phone">
                       Contact phone:
</label>
              
</th>
              
<td>
                  
<input type="text" id="contact_phone" name="contact_phone" />
              
</td>
          
</tr>
          
<tr>
              
<th>
                  
<label for="contact_address">
                       Contact address:
</label>
              
</th>
              
<td>
                  
<input type="text" id="contact_address" name="contact_address" />
              
</td>
          
</tr>
          
<tr>
              
<th>
                  
<label for="contact_firm">
                       Firm name:
</label>
              
</th>
              
<td>
                  
<input type="text" id="contact_firm" name="contact_firm" />
              
</td>
          
</tr>
          
<tr>
              
<th>
                   Code:
              
</th>
              
<td>
                  
@if (ViewData["ReCaptchaSuccess"] != null && !(bool)ViewData["ReCaptchaSuccess"])
                   {
                      
<strong><span style="color: red;">Captcha Validation FAILED!</span></strong>
                   }
                  
@Html.Raw((string)ViewData["ReCaptchaScript"])
               </td>
          
</tr>
          
<tr>
              
<th>
              
</th>
              
<td>
                  
<input type="submit" name="submit" value="submit" /><br />
              
</td>
          
</tr>
      
</tbody>
  
</table>
  
</form>
</div> 

Also you need to add this plugin on your view:

ReCaptcha plugin return next values: