Wordpress JSON API returns normal site page in html. How do I get it to give me JSON like it's supposed to

I'm likely doing it wrong, but when I form my requests for a Wordpress installation at http://www.example.com/ like this:

http://www.example.com/index.php?rest_route=/my/rest/route/here

I end up getting proper responses back.

I had a heck of a time figuring this out and ended up grokking a URL formatted like that in the HTML returned to me. I was expecting to make requests as http://www.example.com/wp_json/wp/v2/my/rest/route/here , but I only got HTML responses.

(FWIW, I am reposting this on all similar questions on the StackExchange network. Admins/mods - if this is against the rules or seen as rep spamming, feel free to take it down. Was hoping to help anyone else hitting the same issue I am, and to also learn what it is I've done wrong and why.)

Ok, so the new endpoint for Wordpress 4.7 is mywordpresswebsite.example.com/index.php/wp-json. It's part of Wordpress Core as of 4.7 and not a plugin anymore, there's nothing to be activated. Thank you, Mark Kaplun.