Easy method 1:
Move or Copy entire working library from current location to the root of your external drive. Press & hold down shift as you click the icon to start iTunes. Click Choose when prompted, then browse to ..\iTunes\iTunes Library.itl on the external. If you copied the library across then test your new library works properly after renaming the original folder, before deleting the original folder to recover space.
Easy method 2:
If you haven't really started to build your library. Press & hold down shift as you click the icon to start iTunes. Click Create. Browse to the root of the external drive. Drag your media into ..\iTunes\iTunes Media\Automatically Add to iTunes.
Required if you've already tried other things and now have media & library scattered around. See the post make a split library portable.
I moved my iTunes library from my laptop hard drive to an external hard drive. I have a Mac system, so I'm not sure of the key sequence on Windows, but here's what I did.
1. Locate your iTunes library on your machine. In the Apple world, I think it's in your documents folder, but I'm not sure. Once you find it, go up one level from the directory where the iTunes library is (think it's the music directory), copy the whole directory structure to the external hard drive - you can always prune out what you don't want later.
2. When you go to open iTunes on a Mac, if you press the Open Apple (command) key when you click on the iTunes icon, it will prompt you to tell where the iTunes library is that you want to connect to. Pick the location on your external hard drive and then it will always be pointed there.
This worked for me when I moved it off the iMac I had to the hard drive and then when i bought a new computer and connected iTunes to that computer.