How to submit a form

I am new to plugin development.

I have created a page (accessed via shortcode) with a form for the user to fill out. The problem is, when they press the Submit button, it’s taking them to a page that doesn’t exist—and I want them coming back to this page.

Here’s what I’ve got—

<?php

// disable direct file access
if ( ! defined( 'ABSPATH' ) ) {
	exit;
}

// define variables and set to empty values
$nickname = "";

?>

<form method="post" action="<?php echo htmlspecialchars($_SERVER["PHP_SELF"]);?>"> 
Nickname <input type="text" name="nickname"><br>
<input type="submit">
</form>

<?php
echo $nickname;

Any help would be greatly appreciated. Thanks.