How do I implement Toastr JS?

You dont need jquery-migrate. Summarizing previous answers, here is a working html:

<html>
  <body>
    <a id='linkButton'>ClickMe</a>
      
    <script src="http://code.jquery.com/jquery-1.9.1.min.js"></script>
      
    <link href="https://cdnjs.cloudflare.com/ajax/libs/toastr.js/2.0.1/css/toastr.css" rel="stylesheet"/>
      
    <script src="https://cdnjs.cloudflare.com/ajax/libs/toastr.js/2.0.1/js/toastr.js"></script>
      
    <script type="text/javascript">
      $(document).ready(function() {
        toastr.options.timeOut = 1500; // 1.5s
        toastr.info('Page Loaded!');
        $('#linkButton').click(function() {
           toastr.success('Click Button');
        });
      });
    </script>
  </body>
</html>

Toastr is a very nice component, and you can show messages with theses commands:

// for success - green box
toastr.success('Success messages');

// for errors - red box
toastr.error('errors messages');

// for warning - orange box
toastr.warning('warning messages');

// for info - blue box
toastr.info('info messages');

If you want to provide a title on the toastr message, just add a second argument:

// for info - blue box
toastr.success('The process has been saved.', 'Success');

you also can change the default behaviour using something like this:

toastr.options.timeOut = 3000; // 3s

See more on the github of the project.

Edits

A sample of use:

$(document).ready(function() {

    // show when page load
    toastr.info('Page Loaded!');

    $('#linkButton').click(function() {
       // show when the button is clicked
       toastr.success('Click Button');

    });

});

and a html:

<a id='linkButton'>Show Message</a>