i use CS3 - not sure if it's the same or not - but i normally click on the layer i want to edit, then use the marquee tool to select the portion of the element i want to move etc - then i use the move tool to move it where i want it to go. if i really want to make it into two separate elements, i'll hit control-J (or command-J on a mac) to duplicate that part of the layer, and then erase that portion from the original layer ...
hope that helps ?!?