Mocha - unfortunately - does not have a downloadable zip file to help you get started and its browser based tool is deeply buried under its own tests. Extracting it from there takes time and effort.
This writing describes how you can get started with executing your Mocha specs in the browser.
I used the String Calculator Kata as an example. Open up the public/index.html file in your favorite browser and you should see this:
Just type 1,3 in the text box, hit the "Calculate" button and the correct answer appears in green color under the text box.
When you open up the spec/runner.html in the browser, Mocha is happily reporting the test output:
Both Mocha and Should.js are rapidly changing projects. I'd encourage you to download and use the latest source code of those projects as ofter as you can.
I created a Makefile to make this super simple for you. Just run "make" in the project root and you should have the latest version of those files brought to you by node.js and npm.