A WordPress standard contact form and its request mail handler.

form-validate-ajax-call.js

/*----------------------------------------------------------------------------------*/
/* Contact Form AJAX validation and submission
/* Validation Plugin : http://bassistance.de/jquery-plugins/jquery-plugin-validation/
/* Form Ajax Plugin : http://www.malsup.com/jquery/form/
/*---------------------------------------------------------------------------------- */
if (jQuery().validate && jQuery().ajaxSubmit) {

    var submitButton = $('#submit-button'),
        ajaxLoader = $('#ajax-loader'),
        messageContainer = $('#message-container'),
        errorContainer = $("#error-container");

    var formOptions = {
        beforeSubmit: function () {
            submitButton.attr('disabled', 'disabled');
            ajaxLoader.fadeIn('fast');
            messageContainer.fadeOut('fast');
            errorContainer.fadeOut('fast');
        },
        success: function (ajax_response, statusText, xhr, $form) {
            var response = $.parseJSON(ajax_response);
            ajaxLoader.fadeOut('fast');
            submitButton.removeAttr('disabled');
            if (response.success) {
                $form.resetForm();
                messageContainer.html(response.message).fadeIn('fast');
            } else {
                errorContainer.html(response.message).fadeIn('fast');
            }
        }
    };

    $('#contact-form').each(function () {
        $(this).validate({
            errorLabelContainer: errorContainer,
            submitHandler: function (form) {
                $(form).ajaxSubmit(formOptions);
            }
        });
    });
}

wp-contact-form.php

<?php
if ( ! function_exists( 'PREFIX_contact_form_shortcode' ) ) {
	/**
	 * Contact form shortcode
	 */
	function PREFIX_contact_form_shortcode() {

		$target_email = get_post_meta( get_the_ID(), 'PREFIX_contact_form_email', true );

		?>
		<form action="<?php echo esc_url( admin_url( 'admin-ajax.php' ) ); ?>" id="contact-form" method="post">
			<input type="text" name="fname" placeholder="<?php esc_html_e( 'First Name', 'text-domain' ); ?>" title="<?php esc_html_e( '* Please enter your first name.', 'text-domain' ); ?>" class="required">
			<input type="text" name="lname" placeholder="<?php esc_html_e( 'Last Name', 'text-domain' ); ?>">
			<input type="text" name="phone" placeholder="<?php esc_html_e( 'Mobile', 'text-domain' ); ?>">
			<input type="text" name="email" placeholder="<?php esc_html_e( 'Email', 'text-domain' ); ?>" title="<?php esc_html_e( '* Please enter your correct email.', 'text-domain' ); ?>" class="required email">
			<textarea name="message" cols="30" rows="10" placeholder="<?php esc_html_e( 'Message', 'text-domain' ); ?>" title="<?php esc_html_e( '* Please enter your message.', 'text-domain' ); ?>" class="required"></textarea>
			<div class="submission-area">
				<input type="hidden" name="action" value="PREFIX_contact_request"/>
				<input type="hidden" name="nonce" value="<?php echo wp_create_nonce( 'PREFIX_contact_request' ); ?>"/>
				<input type="hidden" name="target" value="<?php echo antispambot( sanitize_email( $target_email ) ); ?>">
				<input type="submit" id="submit-button" value="<?php esc_html_e( 'Submit', 'text-domain' ); ?>">
				<img id="ajax-loader" src="<?php echo get_template_directory_uri() . 'img/ajax-loader.svg'; ?>" alt="<?php esc_html_e( 'Ajax Loader', 'text-domain' ); ?>">
			</div>
		</form>
		<div id="error-container"></div>
		<div id="message-container"></div>
		<?php
	}

	add_shortcode( 'PREFIX_contact_form', 'PREFIX_contact_form_shortcode' );
}

wp-mail-handler.php

<?php

if ( ! function_exists( 'PREFIX_contact_request' ) ) {
	/**
	 * contact form email handler for common contact forms in WordPress
	 * @since   1.0.0
	 * @return  void
	 */
	function PREFIX_contact_request() {

		if ( isset( $_POST['email'] ) ):

			$nonce = $_POST['nonce'];

			if ( ! wp_verify_nonce( $nonce, 'PREFIX_contact_request' ) ) {
				echo json_encode( array(
					'success' => false,
					'message' => esc_html__( 'Unverified Nonce!', 'text-domain' )
				) );
				die;
			}

			// Sanitize and Validate Target email address that is coming from agent form
			$to_email = sanitize_email( $_POST['target'] );
			$to_email = is_email( $to_email );
			if ( ! $to_email ) {
				echo wp_json_encode( array(
					'success' => false,
					'message' => esc_html__( 'Target Email address is not properly configured!', 'text-domain' )
				) );
				die;
			}

			/*
			 *  Sanitize and Validate contact form input data
			 */
			$from_name  = sanitize_text_field( $_POST['fname'] );
			$last_name  = sanitize_text_field( $_POST['lname'] );
			$phone      = sanitize_text_field( $_POST['phone'] );
			$message    = wp_kses_data( $_POST['message'] );
			$from_email = sanitize_email( $_POST['email'] );
			$from_email = is_email( $from_email );
			if ( ! $from_email ) {
				echo json_encode( array(
					'success' => false,
					'message' => esc_html__( 'Provided Email address is invalid!', 'text-domain' )
				) );
				die;
			}

			$email_subject = esc_html__( 'New message sent by', 'text-domain' ) . ' ' . $from_name . ' ' . esc_html__( 'using contact form at', 'text-domain' ) . ' ' . esc_html( get_bloginfo( 'name' ) );
			$email_body    = esc_html__( "You have received a message from: ", 'text-domain' ) . $from_name . ' ' . $last_name . " <br/>";

			if ( ! empty( $phone ) ) {
				$email_body .= esc_html__( "Phone Number: ", 'text-domain' ) . $phone . " <br/>";
			}

			$email_body .= esc_html__( "Their additional message is as follows:", 'text-domain' ) . " <br/><br/>";
			$email_body .= wpautop( $message );
			$email_body .= wpautop( sprintf( esc_html__( 'You can contact %1$s via email: %2$s', 'text-domain' ), $from_name, $from_email ) );

			/*
			 * Email Headers ( Reply To and Content Type )
			 */
			$headers   = array();
			$headers[] = "Reply-To: $from_name <$from_email>";
			$headers[] = "Content-Type: text/html; charset=UTF-8";
			$headers   = apply_filters( "PREFIX_contact_mail_header", $headers );    // just in case if you want to modify the header in child theme

			if ( wp_mail( $to_email, $email_subject, $email_body, $headers ) ) {
				echo json_encode( array(
					'success' => true,
					'message' => esc_html__( "Message Sent Successfully!", 'text-domain' )
				) );
			} else {
				echo json_encode( array(
						'success' => false,
						'message' => esc_html__( "Server Error: WordPress mail function failed!", 'text-domain' )
					)
				);
			}

		else:
			echo json_encode( array(
					'success' => false,
					'message' => esc_html__( "Invalid Request !", 'text-domain' )
				)
			);
		endif;

		die;
	}

	add_action( 'wp_ajax_nopriv_PREFIX_contact_request', 'PREFIX_contact_request' );
	add_action( 'wp_ajax_PREFIX_contact_request', 'PREFIX_contact_request' );

}