To move a selection marque and it's contents use one of the selection tools (ie: the Selection tool, Freehand Selection tool, or the Magic Wand tool), hold down the alt key, press with your left mouse button and drag to the new location. This will move the marque and the contents to the new location and make a new floating layer while leaving the original layer unchanged. To have this work your Selection Mode needs to be set to Replace. The Selection Mode setting is found on the Tool Option Palette.
Another method for moving your selection when using the selection tools is to hold down the Shift key and use your arrow keys or page up or page down keys. This will move the selected pixels to a floating layer and fill the cells on the original layer with the background color. This method works regardless of which Mode is selected. To move the selection and contents and leave the original layer unchanged hold down the control key as well as the shift key while using the arrow keys or page up or page down keys to move the selection.
To move the selection marque only, use the move tool, press with your right mouse button and drag the marque to it's new location.