How to implement polyfills in JavaScript for features that are not supported by all browsers?

A polyfill is a piece of code (specifically written for web applications) that provides modern functionality on older browsers that do not naturally support it. So if a JavaScript method is too new such that some browsers haven't added support for it, you can write a block of code that replicates the methodology in order to prevent your app from breaking on such browsers.

Here are the steps to implementing a polyfill in JavaScript:

In this step, you need to identify the feature(s) that are not supported by all browsers you are aiming to support.

Modern JavaScript uses many features that are not well supported by older browsers or certain versions of browsers. For example:

document.querySelector()

The querySelector() method is not supported in Internet Explorer 8 or earlier versions.

Before applying the polyfill, first check if the current browser supports the feature. This is because the polyfill should only be applied if the feature is not natively supported by the browser.

The "feature detection" technique is commonly used to test for feature support.

if (!document.querySelector) {
  // Polyfill would go here
}

In this example, we are checking if the querySelector() method exists. If it does not exist (!document.querySelector), the polyfill code should be executed.

Once you have checked for feature support, the next step is to implement the polyfill.

A polyfill needs to replicate the native feature as closely as possible.

Here is an example of a rudimentary and partial polyfill for the querySelector method:
```JavaScript
if (!document.querySelector) {
document.querySelector = function(selector) {
var elements = document.getElementsByTagName(selector);
if (elements.length) {
return elements[0];
} else {
return null;
}
};
}
```

This polyfill uses the getElementsByTagName method (which is supported in all browsers) to return the first element with the given tag name. It's a simplistic approach though - it won't work on more complex selectors, only on simple tag selectors.

Once the polyfill has been applied, you can use the feature in your code, just like you would use it if it was natively supported.

You can also use multiple polyfills, if you need to support multiple features. Just make sure you apply them in the correct order.

Once the application is completed, ensure that it functions as expected across all targeted browsers. It’s important to test the application on all targeted browsers to ensure the polyfill works correctly and no additional polyfills are needed.