if i want to move all my music from my computer to my external hard drive can i just drag it onto my external, delete the files from the library and then add them back to the library from the external hard drive?
That should work. Just make sure that in iTunes's preferences under Advanced and the General tab change the "iTunes music folder location" to your external HDD so that any music you may buy/import gets put there as well. That is of course if you let iTunes organize your library (which is recommended).