On your new computer, persumably with a new harddrive and operating system, simply put in your harddrive as a slave, and it should appear in the My Computer ready for you to copy over. If the new operating system is W2000 or XP, any harddrive should work. If the new OS is ME, 98, or 95 it is unlikey a harddrive that has 2000 or XP on it will be accessible, because of file system differences.
But simply taking the harddrive and putting it in a new computer as the master, and only, harddrive is unlikely to work, without reinstalling windows.