Cmd of course temporarily gives you the move tool.
Cmd + Mouse right click will bring up a context menu where you can select a layer.
Cmd + Alt + Shift + Mouse right click will select or deselect the clicked layer.
Cmd + Alt + Mouse left click and drag will copy / move the selected layer
Cmd + Alt + Arrow key will copy / move the selected layer 1px to the direction of your choosing
Cmd + Alt + Shift Arrow key will copy / move the selected layer 10px to the direction of your choosing.