Hi everybody ! Glad to see that some of you could resolve their problem with the link provided by swifer07 so we thank him a lot 
But on my side I kept working on trying to make things more clear and specially after the release of the new FBUnity SDK 4.2.4 so here is what I came up with :
Download Openssl, extract the archive, put the content of bin folder in C:\Program Files\Java\jdk1.7.0_06\bin (or your Java SDK Folder) and execute the following command in Command Prompt (cmd) :
keytool -exportcert -alias androiddebugkey -keystore %HOMEPATH%.android\debug.keystore | “C:\Program Files\Java\jdk1.7.0_06\bin\openssl.exe” sha1 -binary | “C:\Program Files\Java\jdk1.7.0_06\bin\openssl.exe” base64
Of course please think about replacing : *C:\Program Files\Java\jdk1.7.0_06* with you local JDK installation folder path
Important To know also, the right version of openssl tu use on windows 7 x64 with JDK version jdk1.7.0_40 (that’s actually my config) is the version 0.9.8h-1 that you can download in zip format right here
Now to make things clear and easy to understand, you can implement by yourself the SDK in the way that makes it clear for you (skip the example provided within the package you get from the Assets Store).
First thing to do is make sure that you configured your application on facebook and on unity in the right way Facebook Web Games - Unity SDK - Documentation - Meta for Developers
Then just create a new scene, create a single new script where you write down this (after you made sure that you did read it to understand it)
using UnityEngine;
using System.Collections;
using Facebook; // Must be specified to use HTTpMethod class
public class InitAndLoginToFB : MonoBehaviour
{
bool isEnabled;
bool isLogged;
string userId;
Texture pic;
void Awake()
{
isEnabled = false;
isLogged = false;
userId = "not received";
}
private void SetInitFB()
{
// This method method will be called withing the callback received by FB.Init()
isEnabled = true;
}
private void SetAvailability(bool a_status)
{
// This method method will be called withing the callback received each time Unity gets or looses Focus (True/false)
}
void LoginCallBack(FBResult result)
{
if (result.Error != null)
{
Debug.Log("Receive callback login error :: " + result.Error.ToString());
}
else
{
if (FB.IsLoggedIn)
{
// Case login was successful
isLogged = true;
userId = FB.UserId;
}
else
{
// Case login failed (because of cancelling for example)
isLogged = false;
}
}
}
void GetProfilePicAnswer(FBResult response)
{
// This method method will be called withing the callback received by FB.API()
// You can add a control here for any kind of failure to print up a default picture for example
if (response.Texture != null)
{
pic = response.Texture;
}
}
void Start()
{
// Must call FB.Init Once
FB.Init(SetInitFB, SetAvailability);
}
void OnGUI()
{
if (isEnabled)
{
if (!isLogged)
{
if (GUI.Button(new Rect(5, 5, 100, 40), "Login FB"))
{
// In the string you are sending within the login process you can specify wich "permissions" you are asking for (in this case only to get the user's email)
FB.Login("email", LoginCallBack);
}
}
else
{
GUI.Label(new Rect(120, 5, 200, 40), userId);
if (GUI.Button(new Rect(5, 5, 100, 40), "GetPic"))
{
FB.API("/me/picture", HttpMethod.GET, GetProfilePicAnswer);
}
}
if (pic != null)
{
GUI.DrawTexture(new Rect((Screen.width - pic.width) / 2, (Screen.height - pic.height) / 2, pic.width, pic.height), pic);
}
}
}
}
