Read the forum posts at:
For moving ALL photos, it is recommended you do that using COPY in the Operating System (Lightroom shut-down).
And use the OS to compare the copy to insure all files have copied correctly.
Open Lightroom, then with the new drive connected- use the "Update Folder Location" to point the top-most photo folder to the new location. This will re-link all photos in their new location. Later the 'old' photo versions can be deleted from the internal drive. (and you do have other backups -naturally!)
"Space on the desktop."
Windows computers have a limit to the number of files that can exist on the desktop (including any folders) so it is a poor idea to use the Desktop for storage. Better to use a folder like "Documents", etc, or the external drive as you are intending.
When moving a large number of files, like a folder tree, it is best to do this outside of Lightroom using OS tools Finder or Explorer.
Copy the files to the new location.
After you have verified that the images are successfully there, you can delete the files from the old drive.
Then, in Lightroom, Library module, Folder panel, use the "find missing folder" or "relocate folder" commands from the right-click menu.
- Update Folder Location
- Delete originals once you are 100% sure everything is working properly
- Delete originals
- Find Missing Folder
I think it's safer to delete the originals photos at the end of the process once you are sure you have done everything properly, rather than in the middle of the process. There's no extra work involved to obtain the slight extra safety of the first method.