Tap and hold on the desktop to bring up the context menu.  Rearrange Mode is a toggle style menu item.  When a check mark is next to it, items on the desktop can be moved with the stylus. 

Moving screen items with the stylus takes a little practice.  If you release pressure while moving the stylus the item will stop moving.  We recommend that you practice moving an icon around on the screen with your device on a table top to hold it steady.  Once you have mastered this approach, try holding the device in your hand and moving an icon around.

It also helps to have a clean screen.  Areas with dust and small specs can make the stylus release pressure on the screen causing the icon to stop moving.