Do a search on Bimmerforums, or you can even Google it and the specific thread should show up. My computer says that the search database is down, maybe you'll have some luck.
Search for "E34 Broken Door Handle Repair"
You are looking for the result of "Door Handle Repair in a Million Easy Steps" it's a very detailed photographic procedure by "Red Five", who used to be on this board long ago.
Anyway, you have to remove the lock cylinder to replace the handle, what you need to do is simply swap the cylinder into the new door. There's a trick about keeping the key in the cylinder when you take it loose from the mechanisims or else the wafers and springs go flying everywhere. Find the post and study it. Wish I could link you to it, but I'm unable. Since you will have 2 doors to practice on, (you have to take it apart anyway) you'll be experienced enough to switch the lock cylinders with no problem. Just remember it's labor intensive, but you'll be fine following the procedure. Just allow plenty of time and patience.
When you get done, have the old handles engraved with "BMW Motorsport" and send them to me...=)
Good luck,
JR