First time trying to use API and OAuth @DigitalOcean

I am trying to make application that will use Digital ocean api to create/monitor/modify droplets/vps. I have never done anything like this, but i have general idea of how api's work (experimented with Reddit's api to show subreddits/comments).

But i don't know how authentication works, do user have to authenticate only once, and then i save some kind of a key in database to use it later? I was hoping to make it in a way user will authenticate it first time he logins on site, and then wont have to never again.

How should i start this, what to use.. ? I was thinking of using this. Any hints and tips are welcome :)