config.cs

internal static string GoogleAppId = "your google app id";

internal static string GoogleAppSecret = "your google app secret";

internal static Uri GoogleStartUri = new Uri("https://accounts.google.com/o/oauth2/auth?client_id=" + Uri.EscapeDataString(GoogleAppId) + "&redirect_uri=" + Uri.EscapeDataString("urn:ietf:wg:oauth:2.0:oob") + "&response_type=code&scope=" + Uri.EscapeDataString("profile https://www.googleapis.com/auth/plus.login https://www.googleapis.com/auth/plus.me email"));

internal static Uri GoogleEndUri = new Uri("https://accounts.google.com/o/oauth2/approval?");

GetGoogleSuccessCode.cs

private string GetGoogleSuccessCode(string data)
{
    if (string.IsNullOrEmpty(data)) return null;
    var parts = data.Split('=');
    for (int i = 0; i < parts.Length; ++i)
    {
        if (parts[i] == "Success code")
        {
            return parts[i + 1];
        }
    }
    return null;
}

GetToken.cs

public async Task<string> GetToken(string code)
{
    var client = new HttpClient();
    var auth = await client.PostAsync("https://accounts.google.com/o/oauth2/token", new FormUrlEncodedContent(new[]
    {
        new KeyValuePair<string, string>("code", code),
        new KeyValuePair<string, string>("client_id",Config.GoogleAppId), 
        new KeyValuePair<string, string>("client_secret",Config.GoogleAppSecret), 
        new KeyValuePair<string, string>("grant_type","authorization_code"),
        new KeyValuePair<string, string>("redirect_uri","urn:ietf:wg:oauth:2.0:oob"),  
    }));
    
    var data = await auth.Content.ReadAsStringAsync();
    Debug.WriteLine(data);
    var j = JToken.Parse(data);
    var token = j.SelectToken("access_token");
    return token;
}

login.cs

#if WINDOWS_APP
    var auth = await WebAuthenticationBroker.AuthenticateAsync(WebAuthenticationOptions.UseTitle, Config.GoogleStartUri, Config.GoogleEndUri);
    Debug.WriteLine(auth.ResponseData);
    
    var successCode = GetGoogleSuccessCode(auth.ResponseData);
    var token = GetToken(successCode);
    //do something with the authentication token
#else
    WebAuthenticationBroker.AuthenticateAndContinue(Config.GoogleStartUri, Config.GoogleEndUri, null, WebAuthenticationOptions.UseTitle);
#endif