The default action for drag and drop in the GNOME File Manager is to move files. But you can alos use drag and drop to copy a file by pressing the CTRL key while moving the files. This will work the same for any files you drag to the desktop. Keep that in mind when you are dragging files such as an executable program you may not want to actually reside on your desktop.
Selecting files to move or copy is done with your mouse by clicking on the file or files in the GNOME File Manager. The file that is selected will then highlight to show you that it has been selected. There are a couple of ways to select more than one file. One way is to use the "rubber band" select by dragging the mouse cursor around several files. This action will produce a small dotted line, the "rubber band", to show you the area in which files will be selected. If you wish to be more selective about the files you are choosing, or the files you need do not reside next to one another, you may use the CTRL key to keep the files you have selected while you are selecting more. This works by selecting a file, pressing and holding the CTRL key and selecting another file. While the CTRL key is pressed you will be able to add to the "list" of files that are selected. Once you have selected multiple files by either method you may copy or move the files as referenced above.
Another way to copy or move files is to take advantage of the right mouse click pop-up menu. Right mouse click on the file you want to copy or move and select Move/rename or Copy from the pop-up menu. This will bring up a dialog in which to perform these tasks.
If the file you are moving has a symbolic link (which is a virtual link to where the file actually lives) associated with it you may select the Advanced Options tab and select Preserve symlinks. Selecting this will make sure the link is preserved despite the move. It is recommended that you use this method of moving a file if it has a symbolic link associated to it.