Followed this official tutorial, my own version on GitHub, and you can see it in action here (click the cube to see the effect).

Steps on how to make this:

1. Create a new 3D project
2. Save the scene as Level0
3. Create -> 3D object -> Cube
4. Create -> Light -> Directional light
5. Save this scene and create a new one Level2 and repeat the process just here create two cubes
6. Create an empty object called FaderObj and attach a new script to it called Fading:

   #pragma strict
   
   public var fadeOutTexture : Texture2D;	// the texture that will overlay the screen. This can be a black image or a loading graphic
   public var fadeSpeed : float = 0.8f;		// the fading speed
   private var drawDepth : int = -1000;		// the texture's order in the draw hierarchy: a low number means it renders on top
   private var alpha : float = 1.0f;			// the texture's alpha value between 0 and 1
   private var fadeDir : int = -1;			// the direction to fade: in = -1 or out = 1
   
   
   function OnGUI()
   {
   	// fade out/in the alpha value using a direction, a speed and Time.deltaTime to convert the operation to seconds
   	alpha += fadeDir * fadeSpeed * Time.deltaTime;
   	// force (clamp) the number to be between 0 and 1 because GUI.color uses Alpha values between 0 and 1
   	alpha = Mathf.Clamp01(alpha);
   	
   	// set color of our GUI (in this case our texture). All color values remain the same & the Alpha is set to the alpha variable
   	GUI.color = new Color (GUI.color.r, GUI.color.g, GUI.color.b, alpha);
   	GUI.depth = drawDepth;																// make the black texture render on top (drawn last)
   	GUI.DrawTexture(new Rect(0, 0, Screen.width, Screen.height), fadeOutTexture);		// draw the texture to fit the entire screen area
   }
   
   // sets fadeDir to the direction parameter making the scene fade in if -1 and out if 1
   public function BeginFade (direction : int)
   {
   	fadeDir = direction;
   	return (fadeSpeed);
   }
   
   // OnLevelWasLoaded is called when a level is loaded. It takes loaded level index (int) as a parameter so you can limit the fade in to certain scenes.
   function OnLevelWasLoaded()
   {
   	//alpha = 1;		// use this if the alpha is not set to 1 by default
   	BeginFade(-1);		// call the fade in function
   }

7. Add the following script to the Cube object:

   #pragma strict
   
   var counter = 0;
   function Start () {
   
   }
   
   function Update () {
   
   }
   
   function OnMouseDown(){
   	Debug.Log("clicked " + counter++);
   	var fadeTime = GameObject.Find ("FaderObj").GetComponent(FadingJS).BeginFade(1);		
   	
   	yield WaitForSeconds(fadeTime);	
   	
   	GameObject.Find("Cube").renderer.enabled = false;
   	
   	fadeTime = GameObject.Find ("FaderObj").GetComponent(FadingJS).BeginFade(-1);
   	
   	yield WaitForSeconds(fadeTime);	
   	
   	Application.LoadLevel(Application.loadedLevel + 1);	
   }

8. Drag a 2×2 black png image to the Texture variable in the Fading script.