Fiz uma classe de solicitação posterior que eu poderia reutilizar para fazer solicitações POST para uma API externa e retornar os objetos que eles me enviaram (JSON):

class PostRequest
    {
        private Action<DataUpdateState> Callback;

        public PostRequest(string urlPath, string data, Action<DataUpdateState> callback)
        {
            Callback = callback;

            // form the URI
            UriBuilder fullUri = new UriBuilder(urlPath);
            fullUri.Query = data;

            // initialize a new WebRequest
            HttpWebRequest request = (HttpWebRequest)WebRequest.Create(fullUri.Uri);
            request.Method = "POST";

            // set up the state object for the async request
            DataUpdateState dataState = new DataUpdateState();
            dataState.AsyncRequest = request;

            // start the asynchronous request
            request.BeginGetResponse(new AsyncCallback(HandleResponse),
                dataState);
        }

        private void HandleResponse(IAsyncResult asyncResult)
        {
            // get the state information
            DataUpdateState dataState = (DataUpdateState)asyncResult.AsyncState;
            HttpWebRequest dataRequest = (HttpWebRequest)dataState.AsyncRequest;

            // end the async request
            dataState.AsyncResponse = (HttpWebResponse)dataRequest.EndGetResponse(asyncResult);
            if (dataState.AsyncResponse.StatusCode.ToString() == "OK")
            {
                Callback(dataState); // THIS IS THE LINE YOU SHOULD LOOK AT :)
            }
        }
    }

    public class DataUpdateState
    {
        public HttpWebRequest AsyncRequest { get; set; }
        public HttpWebResponse AsyncResponse { get; set; }
    }
}

o método de retorno de chamada obtém o objeto datastate e o envia para essa função:

    public void LoadDashboard( DataUpdateState dataResponse )
    {
        Stream response = dataResponse.AsyncResponse.GetResponseStream();
        //Encoding encode = System.Text.Encoding.GetEncoding("utf-8");
        //StreamReader readStream = new StreamReader(response, encode);
        //readStream.Close();


        Deployment.Current.Dispatcher.BeginInvoke(() => {
            App.RootFrame.Navigate(new Uri("/Interface.xaml", UriKind.RelativeOrAbsolute));
        });
    }

Agora não tenho certeza de como obter o corpo da resposta que me foi enviada pela API. Ele está retornando um formato json, eu preciso ser capaz de mapeá-lo para uma boa classe c # e usá-lo para exibir coisas no telefone.

Não consigo encontrar um exemplo que não use JSON.NET (que não possui um assembly para o windows phone 8)

Este é o erro que eu começo a instalar a classe HTTPClient:

Attempting to resolve dependency 'Microsoft.Bcl (≥ 1.1.3)'.
Attempting to resolve dependency 'Microsoft.Bcl.Build (≥ 1.0.4)'.
Successfully installed 'Microsoft.Bcl.Build 1.0.10'.
Successfully installed 'Microsoft.Bcl 1.1.3'.
Successfully installed 'Microsoft.Net.Http 2.2.13'.
Successfully added 'Microsoft.Bcl.Build 1.0.10' to UnofficialPodio.
Executing script file ***\packages\Microsoft.Bcl.Build.1.0.10\tools\Install.ps1'.
This reference cannot be removed from the project because it is always referenced by the compiler.
This reference cannot be removed from the project because it is always referenced by the compiler.
This reference cannot be removed from the project because it is always referenced by the compiler.
This reference cannot be removed from the project because it is always referenced by the compiler.
Executing script file ***\packages\Microsoft.Bcl.Build.1.0.10\tools\Uninstall.ps1'.
Successfully uninstalled 'Microsoft.Bcl 1.1.3'.
Successfully uninstalled 'Microsoft.Bcl.Build 1.0.10'.
Install failed. Rolling back...
Failed to add reference to 'System.IO'.

"{
    \"access_token\": \"123803120312912j\",
    \"token_type\": \"bearer\",
    \"ref\": {
        \"type\": \"user\",
        \"id\": 123123
    },
    \"expires_in\": 28800,
    \"refresh_token\": \"234234f23f423q432f\"
}"

...

public class Auth
{

    [DataMember(Name = "access_token")]  
    public string AccessToken { get; set; }

    [DataMember(Name = "token_type")]  
    public string TokenType { get; set; }

    [DataMember(Name = "expires_in")]  
    public string ExpiresIn { get; set; }

    [DataMember(Name = "refresh_token")]  
    public string RefreshToken { get; set; }

    //[DataMember(Name = "ref")]  
    //public string Ref { get; set; }

}