I am not certain if you are referring authenticating to an API via Angular or just API auth in general, but I can touch on both.
atm, we just use traditional rails authentication since our angular app is the only consumer of the api. But, that will be a bridge we need to cross soon and will post our findings. I would start by looking at how other market leaders do it, eg Stripe et al.
As far as connecting an angular app to backend api, I would look at this http://www.frederiknakstad.com/authentication-in-single-page...