Build your know contact form and add to database.

Step1; Create a table name wp_contact

CREATE TABLE IF NOT EXISTS `wp_contact` (
  `id` int(5) NOT NULL AUTO_INCREMENT,
  `contact_name` varchar(50) NOT NULL,
  `contact_email` varchar(50) NOT NULL,
  `contact_subject` varchar(50) NOT NULL,
  `contact_message` varchar(200) NOT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB  DEFAULT CHARSET=latin1 AUTO_INCREMENT=1 ;

Step2. Create a template and add below code.

<?php
/**
Template Name: contact
 *
 * @link https://codex.wordpress.org/Template_Hierarchy
 *
 * @package WordPress
 * @subpackage Twenty_Thirteen
 * @since Twenty Thirteen 1.0
 */

get_header(); ?>
<?php
if(isset($_POST['submit'])){
        global $wpdb;       
        $name = $_POST['fname'];
        $email = $_POST['email'];
        $subject = $_POST['subject'];
        $message= $_POST['message'];
               
       $wpdb->insert(
        'wp_contact',
        array(
        'contact_name'=>$name,
        'contact_email'=>$email,
        'contact_subject'=>$subject,
        'contact_message'=>$message));

        // mail function
        $to="admin@gmail.com";
        $body = $_POST['message'];
        $headers = array('Content-Type: text/html; charset=UTF-8');       
         wp_mail( $to, $subject, $body, $headers );
        echo "<center'>Success Send</center>";
}
?>

<div class="author-info">
  <div class="container">
    <div class="center">
      <h2>Drop Your Message</h2>
    </div>
    <div class="row contact-wrap">
      <form id="demo-form" class="contact-form" name="contact-form" method="post" action="">
        <div class="col-sm-5">
          <div class="form-group">
            <label>Name *</label>
            <input type="text" name="fname" class="form-control" required>
          </div>
          <div class="form-group">
            <label>Email *</label>
            <input type="email" name="email" class="form-control"required>
          </div>
        </div>
        <div class="col-sm-5">
          <div class="form-group">
            <label>Subject *</label>
            <input type="text" name="subject" class="form-control" required>
          </div>
          <div class="form-group">
            <label>Message *</label>
            <textarea name="message" id="message" required class="form-control" rows="8"></textarea>
          </div>
        </div>
        <div class="form-group">
          <input type="submit" name="submit" value ="Submit" class="btn btn-primary btn-lg" required="required">
        </div>
      </form>
    </div>
    <!--/.row-->
  </div>
</div>
<!-- #primary -->
<?php get_sidebar(); ?>
<?php get_footer(); ?>