Do you mean what you see in Media Library in WMP9?
There is a file called CurrentDatabase_59R.wmdb which stores all that information.
You need to show Hidden Files on the old computer. For Windows ME, 2k or XP, in My Computer, click Tools, Folder Options, View tab, and tick Show hidden files and folders. Click OK.
Search for that file (or files with .wmdb extension) on your old computer, or if you use Windows XP, it might be in the folder C:\Documents and Settings\[YourUserName]\Local Settings\Application Data\Microsoft\Media Player
Copy the file, and put it in the same corresponding folder on the new computer, replacing, if any, the existing currentdatabase_59R.wmdb file. Note that if you have entered any information in WMP9 on the new computer, you will lose that information.
Note also that the file includes the location of the music tracks (including the drive letter), which can't be edited. Not sure what it will do with external drives. So it might help if you can change, if necessary, the drive letter for the external drive on the new computer to the same letter as is used on the old computer, so that when you try to play a track from the external drive, there won't be any problem finding the file in the right drive.