all you do is point them at the external drive when they ask where the library is.
CZ is correct, you can do that, but that would mean that any further content you add would be stored on the external HDD, rather than the internal HDD of your new machine – it will also leave you without a backup.
If you buy a machine with a decent capacity HDD, you can store your iTunes library on there – then use the external as a back-up as you have been doing.
All you need to do for the above is to install iTunes on your new machine (it will create a folder for itself when it does so), then drag all the content from the external into the itunes window (top-left “library” section). It will then copy the media from the external to the default folder on the internal HDD.
If you are on a PC, I can’t remember if dragging and dropping works – you might need to go file > library > add to library, or something.
It doesn’t qualify as “cheap”, but if you are primarily using your home PC for music/photos/web – consider looking at a mac. Mac-hating is popular on STW….. so I will leave it as a gentle suggestion for fear of being lambasted and labeled a brainless fanboi 🙂
edit: just read CZs post again, and i think iTunes gives you the option of “hunting” for music on your HDD when you install it from scratch, which is probably what he’s referring to (apologies). If this is the case just check that it’s copying those files from the external to the (default) itunes folder on the internal – not just referencing them. There is an option in preferences called “let iTunes keep my folder/collection organised” or something – make sure this is checked.