location of new Icons to the desktop
Control click on the desktop away from any icon and select Clean Up By and choose one of the options. This will test that the desktop file is viable. 

If it isn't you can delete it or run Disk Utility to repair the volume

Open terminal and type

rm ~/Desktop/.DS_Store


Then try to move icons or clean up again. You can then choose to keep things arranged or use clean up periodically or arrange them by hand.