Click on any block, then on the 'control' menu icon on the left and you will see the 'Classname' option in the dropdown. Try adding a note note-notice class to any text block and see the result.
<!DOCTYPE html>
<html>
<head>
<title>Redactor</title>
<meta charset="utf-8">
<!-- css -->
<link rel="stylesheet" href="/your-folder/redactor.css" />
</head>
<body>
<!-- element -->
<textarea id="entry">...</textarea>
<!-- js -->
<script src="/your-folder/redactor.js"></script>
<script src="/your-folder/plugins/blockclass/blockclass.js"></script>
<!-- call -->
<script>
Redactor('#entry', {
plugins: ['blockclass']
});
</script>
</body>
</html>