The only "trick" is to make sure you have the setting that puts all the music in the itunes library. There are two settings, one which just links to any music on your computer and the other to move/copy all of it into your library. I think it's "Keep itunes music folder organized" or something like that. With that setting your itunes purchases and any other music content on your computer that you added to itunes (directly or by itunes just finding it) will be copied into the library. If you are using itunes to do the ripping, there's no problem, but if you are ripping with something else and putting the files where you want them, you can end up with two copies of the files. Not a big deal if you have enough space, but you should be aware of that. (I rip to a lossless format and then use dbpoweramp to convert to mp3, then import the mp3s to itunes. You can do something similar with itunes.)

There's a FAQ for this on the apple support web site. Here's the one for windows. There's a link in the article to the FAQ for macs.

http://docs.info.apple.com/article.html?artnum=93366

Basically, once you have made sure you have the "Keep itunes music folder organized" set, you just copy the library to the external hard drive and then you can import it into itunes on the other computer. Or if you don't have itunes on the other computer yet, you can just drop it into the right place, then download itunes, and it should just find it and use it once you authorize the new computer.

You can use your ipod as the external hard drive if there's enough free space on it.

-David