The following should work. Just finished testing it on mine, though I've not been able to test the transfer to another account. I am making a big assumption that you are using Windows and that neither of you use an Apple computer. I don't know if that changes anything.
First, go to the tailor's / facemaker's, select the costume you'll need. Save the costume using the save feature in the top right corner of the costume screen. I chose to give mine a special name to track more easily. Then:
1. Go to your computer's Explorer (In Windows XP, like mine, just right click on the START button, and select Explorer.
2. Navigate to your game files. Your default is probably C:\Program Files\City of Heroes.
3. Look for the folder called "Costumes". Open this and find the file for the costume you just created. Note that the extension is called ".costume". Copy this file and send it to your friend.
The receiver does the following:
1. copies the .costume file to his or her Costumes folder (same locations as 2 and 3 above)
2. start the game, go into the MA designer and follow the steps for creating a custom character.
3. when the costume screen appears, select the "Load" button in the top right. Select your costume and load it.
4. complete the character's design. When you save the results it will save the MA character under the folder "Custom_Critter" and it will be a ".critter" file. The original ".costume" file will remain in the costume folder.
He's on windows, I'm running on a mac. If that makes any diff. Will try it anyways, as I know my way around a mac decently, just was wondering if it'd work and what the file extensions for this stuff are. Thx a bunch for your help.
The files you are looking for is located in the CoX application. "Applications - Show Package Files" and then you can navigate to the costume folder in there. While I'm at work I can't guide you directly but finding the files are as easy as goblin pie.
I love how mac does everything better then a PC (referring to keeping all of the applications files in one single icon) 
The files is the exact same formats because Macs CoX client is an emulated windows client using Cider from Transgaming. Just remember that he can't use the costume if you have pieces in it from an expansion that he have not yet activated or if he's too low level for certain stuf (capes, auras) 
A friend of mine really likes the look of one of my toons and wants to know if theirs a way I could possibly send him the file of her appearance/costume to him so he can use it as a custom final boss for one of his MA arcs. I know you can save a costume file during creation or while at the tailors, and easily upload your own saved files as alt costumes. What I'm wondering is if there's a way to save her primary look, then find that file info and send it to my friend so he can load it into his MA for his custom final boss.