You should be able to simply drag/drop the folders from the folder tree in the library module to your network drive. Pay attention to the progress bar in the top left-hand corner of the Lightroom screen and make sure that you don't close Lightroom while the transfer is in progress.
The other method would be to use your system browser (Explorer or Finder) and move your images to the network drive. Then you would follow the instructions below on how to relink Your images.
Follow these three steps:
- Using your operating system, COPY (not MOVE) the photos to the network drive.
- Follow these instructions to allow LR to recognize and use the files on the network drive (scroll down to the section that is entitled "Updating Folder Location") Adobe Lightroom - Find moved or missing files and folders
- When you are 100% sure you have gotten the first two steps working properly, delete the photos from your original HD.
I would suggest you to make a main folder with all the other image folders in Lightroom and then move the main folder to the network drive.
As you move the images from current location to network, you will get an exclamation mark on the main folder that you created so you can just locate the main folder.