Dragging within LiveCode is accomplished by the various drag messages that are available. An example of this if you have two images on your stack would be-
Script of image 1
on dragStart
set the dragData["text"] to the text of image 1
set the dragImage to the id of me
end dragStart
Script of Image 2
on dragEnter
set the dragaction to "copy"
end dragEnter
on dragDrop
set the text of the target to the dragData["text"]
end dragDrop
When image 1 is clicked and dragged, its text (contents) are placed into the dragData array, its dragAction is set to copy and the drag image is set to the image id of itself. THis is the transparent image that indicates what you are dragging.
In image 2, when a user is dragging and enters the image, it sets the acceptDrop to true and when the user releases the mouse (dragDrop) the text of the image is set the to the dragData["text"] array