You can check out Chapter 8 of RESTful.NET ( Amazon , Google books )
You will only authenticate the first call from the user, any subsequent calls will use the context of the authenticated user. There are several options for using SSL (TLS), as always or simply when sending a username / password.
I am not sure exactly where and how you store the authentication token (for example, in a session or similar type).
You do not need to use the ASP.NET membership provider, in fact you cannot use any member provider at all, just use other authentication models. Typically, there will only be one authentication model per service, for example, you get credentials, check them for permanent storage, if in reality you set a security token, and this token is used for all of the following calls for a limited time.
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