I thought the documentation wasn't entirely clear too, but I figured it out eventually and got it set up. Here's how:
Include the Mocha script and CSS in Index.html. Also include a div with id "Mocha" for the output to be inserted into. Include the test script you'd like to execute.
<link href="lib/mocha/mocha.css" rel="stylesheet" />
<script src="lib/mocha/mocha.js"></script>
<script src="test/my_mocha_test.js"></script>
<div id="mocha"></div>
In your test file (my_mocha_test.js in this example) include this setup line at the top:
// 'bdd' stands for "behavior driven development"
mocha.setup('bdd');
Now with the test and the Mocha content all loaded, you can run the tests with this command:
mocha.run();
You can add that to an event listener and trigger it on a button push or other event, or you can just run it from the console, but it should put the test output in the div with the "mocha" id. Here's a page with all this set up with code viewable on GitHub for you to
https://captainstack.github.io/public-stackhouse/