Before you start getting into any separate, third-party authentication app you might find it much easier to just start with one app and set up two-factor authentication on just that app. You have to use apps that support whichever third-party authentication app anyway, so instead of starting with the more involved approach, start with one app first, get familiar with how it works, and then move on to something more advanced.
Try enabling this on your Google account by following these directions:
https://support.google.com/accounts/answer/185839?co=GENIE.Platform=Android&hl=en&oco=1
Once you get that set up, log in and out of your Google account so you see how it works. Then try enabling two-factor authentication on another app, like your text messaging app and get used to how that works. If you then want to implement a third-party service to manage multiple logins, just keep in mind that this isn't a universally-applied thing that works with very app, it's only apps that require a user log in authentication and those apps have to support that chosen service.