The simplest way to go about doing this is as follows:
- Make a playlist (not a smart playlist) in iTunes for exporting purposes. Call it whatever you'd like.
- Drag and drop the content from the source iTunes into that playlist.
- Create a folder on your transfer media of choice (network share, USB drive, whatever) to put the migrated files in.
- Select everything in that transfer playlst.
- Resize the iTunes window, if necessary, so you can see the media and iTunes at the same time.
- Drag and drop the items from that playlist into your transfer folder.
- Wait until iTunes completes the copy job.
Then, on the destination iTunes, drag and drop the transfer folder onto the main iTunes Window, where it says Music. Done!
All you must do now is recreate playlists and such.