i have cheated a little bit... i moved to the editor on my PC to add the units because the Mac editor tends to not save information well. Additionally, the PC editor allows for the placement of cities to create a real scenario with truer start locations, etc. However, adding units is incredibly easy. Some things to keep in mind though are:
Definitely use the editor that AlanH has provided if you are working on the Mac (both the TextEdit as well as the CivEdit).
When you add a unit, make sure that the name you choose for the unit in the box that appears when you click the "add" button, is identical to the name of the folder and the subsequent .ini file of the unit you are adding... i had made the mistake, for example, of naming the unit "B52 Bomber" and then putting in the civilopedia box PRTO_B52 which coincided with the name of the unit and the .ini file. But this was not working. When i changed the name of the folder the unit was in, as well as the .ini file to "B52 Bomber" then it worked. A pretty simple thing, but frustrating if you didn't know about this.
You only have to add the unit to the PediIcons file, it is not necessary to add it to the civilopedia file.
A good way to test the unit to make sure it is in working order is to save a test .bic with the unit not needing any resources or prerequisites, make you civilization begin as a republic and give it money enough to purchase the added units outright. If the units show up, and you do not get an error message when you click on them to buy, then chances are they are going to work. Go ahead and buy them though and try them out.
If the game crashes at startup or crashes when you select the unit to purchase it, then you have probably failed to use the TextEdit supplied by AlanH. Open the file again and save it with CR/LF option clicked. Try it again and things should work.
After you know things are working, then go back and set the values for the unit that you want (prerequisites and resources needed for it, etc.) Adding the unit to the units32.pcx file (i used photoshop) will allow it to be seen when you are buying it, but i have not been able to get it to show up in the civilopedia as a picture--i just get a pink box).
It seems frustrating at first, but once you figure out to keep the name the same, and to make sure that you are saving the file correctly then relatively simple.