Moving a slab is fairly simple. First, you select your slab portion you want to share.
Just left-click on the map and drag your mouse to draw a box on the grid. Once you have selected the area you want, let up on the mouse button and continue dragging to select vertically. You can also click on the small boxes on the sides of your selection to adjust the size. Left-click to complete your selection.
Ctrl-X will then cut it and let you move it with your mouse. Move to where you want and left click to drop it in place.