What steps are involved in using polyfills to debug JavaScript compatibility issues across older browsers?

Identify the specific JavaScript features that aren't working in an old browser. You may have a strong suspicion about some features, but it's important to test thoroughly. Use a tool like BrowserStack to test multiple versions of many different browsers quickly.

• Test the site on the problematic browser(s) and note down the issues.
• Open up the developer console in the browser. Note any error messages that appear here as they will help you determine the cause of the issue.
• Try to narrow down the problem to the smallest reproducible test case. This will save you time in the next steps as it will be faster to test and debug a small, isolated piece of code.

Once you've identified the JavaScript features causing problems, you need to research their browser compatibility. Sites like Can I Use or MDN Web Docs are good resources for this. They will tell you the versions of the major browsers that support the feature, and also if there are any known issues or quirks.

• Research the not working JavaScript features using Can I Use or MDN.
• Note what versions of which browsers should support this feature.

If the problematic JavaScript feature is not supported in the user’s browser, a polyfill can be used to provide that functionality. A polyfill is a piece of code that provides modern functionality on older browsers that do not natively support it.

• You can find existing polyfills using online resources such as the Polyfill service or Polyfill.io.
• When choosing a polyfill, consider the size and performance implications. Also, consider the reliability of the source of the polyfill.

To test the polyfill:

• Integrate the polyfill into your website’s code. Where you place the polyfill in your code depends on how the polyfill is structured and what it’s polyfilling. Generally, it should be loaded before any other scripts.

• Ensure that you conditionally load the polyfill so that it’s only used when needed. This is important to prevent unnecessary code being sent to modern browsers that don’t need it.

• Now test your website in the problematic browser again, the feature should be working now.
• If the feature is not yet working, repeat the process with an alternative solution/polyfill.
• Also, test in modern browsers to ensure that the addition of the polyfill has not caused any new issues. The modern browsers should work as before with no slowdowns or new bugs.

When you are confident the polyfill is working across all necessary browsers:

• Review your code ensuring you didn't break any existing functionalities.
• If everything is in order, then you can deploy your code to production.
• Don't forget to monitor the impact of the change on your site traffic and engagement, and keep an eye on your site's performance and error message logs.

Given that browser vendors release updates continuously and that usage of older browser versions fades over time, you should review the need for each polyfill periodically. If a specific polyfill isn't needed anymore, removing it can reduce your page's loading times and simplify your codebase. It's also worth keeping an eye on newer JavaScript features to see if there might be a future need for new polyfills.