A big part of the REST philosophy is to exploit as many standard features of the HTTP protocol as possible when designing your API. Applying that philosophy to authentication, client and server would utilize standard HTTP authentication features in the API.
Login screens are great for human user use cases: visit a login screen, provide user/password, set a cookie, client provides that cookie in all future requests. Humans using web browsers can't be expected to provide a user id and password with each individual HTTP request.
But for a REST API, a login screen and session cookies are not strictly necessary, since each request can include credentials without impacting a human user; and if the client does not cooperate at any time, a 401
"unauthorized" response can be given. RFC 2617 describes authentication support in HTTP.
TLS (HTTPS) would also be an option, and would allow authentication of the client to the server (and vice versa) in every request by verifying the public key of the other party. Additionally this secures the channel for a bonus. Of course, a keypair exchange prior to communication is necessary to do this. (Note, this is specifically about identifying/authenticating the user with TLS. Securing the channel by using TLS / Diffie-Hellman is always a good idea, even if you don't identify the user by its public key.)
An example: suppose that an OAuth token is your complete login credentials. Once the client has the OAuth token, it could be provided as the user id in standard HTTP authentication with each request. The server could verify the token on first use and cache the result of the check with a time-to-live that gets renewed with each request. Any request requiring authentication returns 401
if not provided.