As written in the page you linked,
"Per-route" rate limits may be shared across multiple, similar-use routes (or even the same route with a different HTTP method). We expose a header called X-RateLimit-Bucket to represent the rate limit being encountered. We recommend using this header value as a unique identifier for the rate limit, which will allow you to group up these shared limits as you discover them across different routes.
... Or in other words, the HTTP response will contain a header called X-RateLimit-Bucket, which will contain an identifying string for the API route you are using. That means that if you were to send thousands of requests to 1 specific API endpoint, Discord will presumably return the same X-RateLimit-Bucket ID in each response.
Along with the X-RateLimit-Bucket header, a few more headers are sent:
X-RateLimit-Limit: 5
X-RateLimit-Remaining: 0
X-RateLimit-Reset: 1470173023
X-RateLimit-Bucket: abcd1234
X-RateLimit-Reset-After: 64.5
The documentation for all these headers are listed in the same page, although the one you should be looking out for here is X-RateLimit-Reset-After and X-RateLimit-Remaining. The 'Remaining' header states how many more requests can you make to this endpoint before you are blocked (429 HTTP error). The 'Reset-After' header states how long you must wait (in seconds) until the current bucket ID will reset, and you will be able to send requests again to this bucket.
In other words, a bucket gets exhausted by you sending requests to it, and it is fully exhausted once the X-RateLimit-Remaining HTTP response header is equal to 0. It automatically resets, and does so after the X-RateLimit-Reset-After HTTP response header is equal to 0 (the seconds you have to wait until you can send requests to that bucket ID is 0).
Update:
As these bits of information are returned as headers, you just have to print the response.headers value to the screen. That will give you all the returned headers. For example, if you want the remaining requests, then you'd execute print(response.headers["X-RateLimit-Remaining"]) (the headers are returned as a dictionary).
However if you are indirectly interacting with the API (using the discord.py module), I'm not sure that this is possible without some edits to the module. After scouring the internet, I haven't managed to find anything that even gets close to exposing the underlying Session object for the module. However, while reading through the request method I found this line, which hints that the module detects the Rate limiting by itself and stops you from sending any requests (if the bucket is exhausted).
