It's very simple.
The checkbox field is like an input text. If you don't write anything in the field, it will say the field doesn't exist.
<form method="post">
<input type="checkbox" name="check">This is how it works!<br>
<button type="submit" name="submit">Submit</button>
</form>
<?php
if(isset($_POST['submit'])) {
if(!isset($_POST['check'])) {
echo "Not selected!";
}else{
echo "Selected!";
}
}
?>