Open up a Node Editor window

(You may also want a UV /Image Editor so you can view the results, link it to the ** Render result**

** **

Switch over to the **  ** compositor****   by clicking on the 3rd icon and check the **Use Nodes** Box

 

 Now setup your nodes like this:

 

Explanation:

You should have 3 Render layers (Add>Input>Render Layers)

2 of these layers should be linked to Scene while the other is linked to Scene.001

The 1st Render Layer should be the Object (find it in the drop down list)

The 2nd Render Layer should be the Shadow (find it in the drop down list)

The 3rd Render Layer should be the Background (find it in the drop down list)

You'll see that there's an extra option for the Shadow Render Layer called AO. This is because you added it to the list of passes that Blender should take into account.

AO must be linked to an Add node (the Add node is actually a mix node that is set to add in the drop down list Add>Color>Mix) The problem here is that the plane doesn't fill the entire image, it just takes up the lower part of it which creates the black surrounding (see it in the preview). The only black area in this scene should be the shadows. To fix this you add an Invert node (Add>Color>Invert) to the Alpha output of the Shadow Layer (the unwanted black part of the image is basically the alpha). So this node inverts the black to white. Then you join the output of the invert node into the other input of the Add node where the AO is connected to. After this you should have a fully white image with just a shadow.

Using the Multiply node(the Multiply node is actually a mix node set to multiply in the drop down list Add>Color>mix) connect the Background layer and Shadow layer (through the add connector).

Before going into othe final Composite node, add an Alpha over node (Add>Alpha Over) to combine the object layer with the other 2. It's important that the Multiply node goes into the top input and the Object Render Layer goes into the bottom one.

Then the output of that goes into the Composite node.

Done! Press F12 to see the final result.

For further enhancements, you could use a curves node (Add>Color>Curves) to brighten or darken each layer to make them fit better. Drag the node's window between the other nodes 'connection' until they turn orange and it will connect itself.

BTW, if the node editor isn't making a difference to the render, make sure that you have the Compositor checked. Go to the Render panel and scroll all the way to the bottom, under Post Processing