A simple example on how to register/login a user via Facebook with Unity and Nakama server.

FacebookManager.cs

/**
 * Copyright 2017 The Nakama Authors
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

using Facebook.Unity;
using Nakama;
using System;
using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class FacebookManager : MonoBehaviour {

    public bool IsLoggedIn {
        get {
            return FB.IsLoggedIn;
        }
    }

    public string CurrentUserId {
        get {
            if (Facebook.Unity.AccessToken.CurrentAccessToken != null) {
                return Facebook.Unity.AccessToken.CurrentAccessToken.UserId;
            } else {
                // Must login via Facebook for a valid access token.
                return null;
            }
        }
    }

    void Awake() {
        if (!FB.IsInitialized) {
            FB.Init(SetInit, SetOnHide);
        } else {
            FB.ActivateApp();
        }
    }

    void Update () {
        if (Input.GetKeyDown(KeyCode.Space)) {
            FBLoginButtonAction();
        }
    }

    private void SetInit() {
        if (FB.IsInitialized) {
            FB.ActivateApp();
        } else {
            Debug.Log("Failed FB SDK init.");
        }
    }

    private void SetOnHide(bool isGameShown) {
    }

    public void FBLoginButtonAction() {
        FBLogin();
    }

    public void FBLogin() {
        var permissions = new List<string> {
            "public_profile",
            "email",
            "user_friends"
        };
        FB.LogInWithReadPermissions(permissions, AuthCallback);
    }

    void AuthCallback(ILoginResult result) {
        if (result.Error != null) {
            Debug.LogFormat("Facebook SDK error: {0}", result.Error);
        } else if (FB.IsLoggedIn) {
            var aToken = Facebook.Unity.AccessToken.CurrentAccessToken;
#if UNITY_EDITOR
            foreach (string permission in aToken.Permissions) {
                Debug.Log(permission);
            }
#endif
            ServerLoginOrRegister(aToken.TokenString);
        } else {
            Debug.Log("Facebook login was cancelled.");
        }
    }

    public void ServerLoginOrRegister(string aToken) {
        var client = NClient.Default("defaultkey");
        var message = NAuthenticateMessage.Facebook(aToken);

        Action<INError> errorHandler = delegate(INError err) {
            Debug.LogErrorFormat("Error: code '{0}' with '{1}'.", err.Code, err.Message);
        };

        Action<INSession> sessionHandler = delegate(INSession session) {
            Debug.LogFormat("Session: '{0}'.", session.Token);
            client.Connect(session, (bool done) => {
                FacebookLink(client, aToken);
            });
        };

        client.Login(message, sessionHandler, (INError err) => {
            if (err.Code == ErrorCode.UserNotFound) {
                client.Register(message, sessionHandler, errorHandler);
            } else {
                errorHandler(err);
            }
        });
    }

    public void FacebookLink(INClient client, string aToken) {
        var message = NSelfLinkMessage.Facebook(aToken);
        client.Send(message, (bool done) => {
            Debug.Log("Successfully linked device ID to current user.");
        }, (INError err) => {
            Debug.LogErrorFormat("Error: code '{0}' with '{1}'.", err.Code, err.Message);
        });
    }

}