Question
I have a tree in the back yard that was butchared from providing shade through out the back yard, to nothing. What I have is a tree stump that has some green growing out of the ends of the tree.

How can I speed up the process to get the green covering whats left of the tree?

Answer
Well one of the worst thing that can be done for a tree is top it and cut all the limbs off. What happens is the tree will sprout back foliage and twigs (that will over time become limbs) but the tree will look like a bush for several years until the limbs start to grow. The original tree shape will take many years to re shape. There is not much that can be done except maybe fertilize the tree with 10-10-10 this Fall and that will encourage more foliage growth next spring. I would wait until the leaves drop this Fall and then add 1 lb of fertilizer per inch of trunk diameter scattered around the tree and watered in good. Apply just before a rain storm and you will not need to water.  Here is a web link on tree topping.
http://www.treesaregood.com/treecare/topping.aspx