Extruding from square to round
I would use a lofted boss/base for this if you want to do it the simple, solid way. Lofted surface would be more appropriate for a more complex surface model, but here's how you loft a solid boss.
Select a plane and create a sketch. In this case I am using the front plane. Draw/dimension your circle. Mine here is 5" diameter, centered at the origin. Exit sketch.
Select the front plane again and click Insert-->Reference Geometry-->Plane. In the dialog box, click on distance and enter the distance that you want between your circle and square. Here I've chosen 6". Click OK.
Select your new plane and create a sketch. Draw/dimension your square. Here I've made it 8" square, centered at the origin again. Exit sketch.
Select Insert-->Boss/Base-->Loft. Right click an empty space on your model window and select Selection Manager.
A small dialog box will open up. Hit Select Closed Loop.
Select your square and click OK in the Selection Manager box.
Select your circle. Click OK in the Selection Manager
You will now see your loft preview (if you have Show Preview selected in the Loft dialog box). Hit Cancel in the Selection Manager.
Click OK for the Loft.
And there it is!