Hi @clma,
Welcome to the Community!
According to the doc you linked:
Auth0 Mobile SDKs and Auth0 Single-Page App SDK: The easiest way to implement the flow, which will do most of the heavy-lifting for you. Our Mobile Quickstarts and Single-Page App Quickstarts will walk you through the process.
Authentication API: If you prefer to roll your own, keep reading to learn how to call our API directly.
In short, yes you are correct! The sdk and quickstart are going to handle the code exchange and all you have to do is fill in the correct client and tenant info.
I would suggest following the quickstarts and SDks if you want to get things up and running quickly or follow the login doc you linked if you want to work directly with the auth server.
Let me know if you have any questions!
Dan