Question
Two weeks ago I planted a 56" tall Blue Italian Cypress that came in a 3.5
gallon container. Soil on the planting site is clay, at least the top few inches
of it and I had problem with watering the tree after planting. Since drought is
becoming bigger problem than rain here in Georgia (I live in Cumming) to
make sure water and air will get to the root system I removed the clay soil
from the top of the root ball and put some crushed pine cones on top of it  
and then covered them with clay, but close to the trunk of the tree I didn't use
the clay soil - I used sand. From the remaining clay I formed a barrier around
the planting site. Since planting I watered it only once. During recent rain I
noticed a puddle of water forming at the base of this tree. From earlier posts
on this site I know that overwatering can be a problem for Italian Cypress.
Should I transplant it to a location with a better drainage, maybe just raise it
higher at the current location, or just fill the puddle with more sand so water
will not accumulate as much? What would be the best course of action?

Answer
I think the problem is the clay that you put on top of the mulch. Sounds like what has happened that the clay is forming like a clay pot and holding the water on top of the ground. Not sure how you planted the tree but here is the best way to plant a tree.
Dig the hole twice the size of the rootball and as deep. Plant the tree so that the ground level in the container is the same as the new ground level. Fill the excess area in the hole with good top soil or potting soil. mulch around the tree (out to about two feet)  with not more than 3 inches deep of organic mulch (pine straw is good) and water.

Since you have just planted the tree and if you  did it different from the above method I would replant the tree as above. Unless the area of the yard where you planted the tree pools water I would replant in the same place. If you think you have dug a good hole I would remove the clay you put around the tree and replace with sand and use a mulch.  

Water once a week if it does not rain with 1 inch of water. Place a pan under the tree and turn the sprinkler on and when the pan has 1 inch of water in it stop. This will deep water the tree and cause the roots to grow deeper than if you daily water a little.