I've done this a bunch of times. Once you get the method down, it's fairly straightforward. The basic steps are as follows:
Let's call your two computers SOURCE and DESTINATION.
1. You are going to want to preserve your file structure during the move to make things easy. Don't try to reorganize the files on disk *and* do a move. Do one or the other.
2. On SOURCE do File > Library > Backup Library . Make note of where this file goes.
3. Copy that backup file to your external drive/SD/whatever.
4. On SOURCE, make a full copy of your Music folder structure onto the external drive. Make sure you understand what the new path looks like. I.E. you should know that it is all under /Volumes/BIG-OL-SD/Music/ . Or whatever the real path may be.
5. Eject the external drive from SOURCE and plug it in to DESTINATION.
6. At this point you should see your whole music folder structure on the external drive on DESTINATION. Make note of the full path. It should be the same as above, but you'll want to be sure.
7. Open MC and do File > Library > Restore Library . Use the backup file that you copied to the external drive in step 3.
8. You should now see everything in MC; all of your albums, artists, playlists, etc. But, all of them will appear to be missing and have a red minus sign (-) next to them. Because MC can't see them in the paths they used to be in.
9. Use the Rename, Move, and Copy files tool to update the file paths.
A. use UPDATE mode.
B. Uncheck everything except for the last section, Find and Replace.
C. Fill out the Find What and Replace With so that the new path to your files is correct. Example:
Find What: /Volumes/Macintosh HD/Users/Fortney/Music
Replace With: /Volumes/Big-Ol-SD/Music
Try this by highlighting ONE FILE. Look at the preview window to make sure things look correct. Once they are correct, press OK. Then check your work. Make sure you can play that file that you updated the path to.
Once this works, do a whole album. Then either do the rest in segments, or just highlight everything remaining and do it in one shot. If you totally screw up, you can start over at step 7.
I've left out some details I'm certain. This is meant to be an overview, as opposed to a full recipe. If you need more information, please ask.
Like I said, I've used this many times to move my library from drive to drive on one Mac, to move my library to another Mac, and even to copy my library to a Linux box running MC. It works really well.
Good luck!
Brian.