Rick, Alex is right on. A few things I can think of...
I did mine the first time with assistance, and second & third times on my own. It's absolutely amazing when it finally comes out as things are quite tight. I don't think there is good pic of this operation, because when it decides to come out is so unexpected.
I supported the car (Plus 2 mind) under the rear floor on very stable blocks. Have a very stable plan for lifting the car as you will probably be hefting things around quite a bit.
I have a Spyder chassis, which provides a bit more clearance. If stock chassis, check carefully before unbuttoning anything that the rear of the chassis is not distorted from incorrect jacking of the car. If this area is bent, it may not come out without bending things to right first. My stock chassis was so distorted I ended up cutting it to remove the diff, and this was with the body off.
Because the diff is not symmetrical, it only comes out the left side of the chassis. Not sure if an issue on the Elan, but on the Plus 2 the long mounting bolts go in from the bottom (nut at top); if not done this way the Plus 2 fuel tank has to be removed.
Other things to check during this job include the handbrake linkage, all diff seals, diff output shafts for distortion of the splines, and adding of the brace Alex mentioned.
If the brace is not already there you can get one from Ray at RD, or pretty sure Dave Bean will have them as well. If adding the brace the spacer washer count will be different to keep diff spaced off of the frame.
There was recently a very helpful thread on the handbrake linkage issues here:
elan-f14/elan-parking-brakes-can-they-made-work-t25716.html