Here's a quick how-to on LSDs
First pick your donor. For 2WD trucks, a 84-85 RX7 will be your best bet. For 4WD, 86-88 Turbo II is your only option.
To remove the diff, disconnect the drive shaft, and remove the rear wheels. Depending on the vehicle, it may be necessary to disconnect the brake lines.
Remove the 4 axle nuts on each side:
Pull out the axles enough to disengage the differential.
Remove all the bolts on the 3rd member case and pull out the diff. You should be left with this:
Here's my old open-diff and new Rx7 diff side by side:
Front view. Note that the long pinion will require a shortened driveshaft. I'm in the middle of a trans swap, so it doesn't matter for me:)
Check for broken spiders. Every Mazda rear I've seen has one broken:
4wd trucks will require some grinding on the diff mounting flange. I took a couple mils off with a grinder at the 2:00, 4:00, 8:00, and 10:00 positions.
Here it is bolted up:
Now it's time for some 2 wheel burnouts