Use iTunes consolidate to a directory on a different drive (Windows and Mac, reorganizes music from any folder to the iTunes\iTunes Media folder under Artist\Album\Song.ext order)
Use Windows to move the Music folder to a different drive and still look like it is on the C Drive (Windows only, moves existing folders to a new drive assumes that all music is already in the Music folder, will not work if music is scattered all over the drive)
Which way seems more applicable to you?
Windows or Mac?
I am assuming that you don't move music files that iTunes knows about with Windows Explorer. If you have done this in the past. Let me know and I can help with steps to let iTunes know where the files are located now. Don't do anything else before we get that fixed.
If you have not moved music files that are also in iTunes, then you are ready to start. I always recommend a backup just in case something goes wrong. At least the iTunes folder and all subfolders should be backed up but if you want to proceed without a complete backup, that is your choice.
In Windows Explorer. create a folder on the other drive.
My suggestion is iTunes Media
long deep paths are trouble, but as long as it is the same length or shorter than the default (Typically C:\Users\<login>\Music\iTunes\iTunes Media), you are good.
In iTunes Edit->Preferences
Go to the Advanced Tab
Note where the original path was (Typically C:\Users\<login>\Music\iTunes\iTunes Media)
Click the Change button.
Select the lowest folder you created (iTunes Media) so the path shows your new drive location
Still in iTunes
Click File->Library->Organize Library
Check the Consolidate files box
Wait for the process to finish.
In Windows Explorer navigate to one directory higher than the original path noted above.
Rename the iTunes Media to OLD this will verify iTunes is not using the old files.
Open iTunes and play Music. Anything you select should play fine.
The original files are still on your C drive. C:\Users\<login>\Music\iTunes\OLD
Once you are convinced the transfer to the new drive worked. you can delete the OLD folder. Leave the iTunes folder where it is as that is where the library still resides. If you need that to be moved to the other drive too (not really necessary to move, as it doesn't take up a lot of space) then ping back and we can go through that too.
There is an iTunes Library.itl in the OLD directory
There is NOT an iTunes Library.itl in the new drive. There are 5 folders (inc Music) and one file called .iTunes Preferences.plist
There is an iTunes Library.itl in the iTunes folder on C Drive
The latest modified is the one in C Drive iTunes but it is 462 Kb, the older one in "OLD" is 2.58 Mb
That was the risk of renaming the folder without knowing where your library file is located.
Using Windows Explorer, navigate to the iTunes folder on the C drive, send the iTunes Library file to the Recycle Bin.
Navigate to the OLD directory and copy the iTunes Library file.
Navigate to the iTunes folder on the C Drive and paste the iTunes Library file there.
All playlists should be there and songs should play.
The cloud signifies the song can be downloaded. Since we hid the original library with the folder renaming, iTunes was showing your purchases from the cloud, not seeing your actual music on the hard drive.