Use REST API without SDK

I know there a PHP SDK but I'd like to know how to authenticate without it. For my private_key I use PostMan and this is what I'm doing. I tried with both "Basic Auth" (public key as username and private key as password) and passing public_key and private_key as POST parameters.

Sorry for the lame question but I'm new with this stuff and I couldn't find anything useful in the forum (mostly because the search box returns zero results if you type less then 4 characters)

PS: in this example I want to show a JSON with all my lists