Alright, high time someone put together a good well written governor swap. However, before you get started, know this. All it does is increase the RPM at which your transmission shifts, it has nothing to do with how much power the engine produces. A mustang governor will not improve your performance at all, it will decrease performance as the engine does not make power past the original shift points. Only highly modified engines benefit from this. IE head swaps, cam swaps, HO's, or anything greater.
Ok so here are a couple pics of an AOD Mustang governor.
Onwards we go.
Fist thing, put the rear of the car on jack stands. But only in the rear. Do not jack the front up. If you do jack the front up to get a little more working room, then jack the rear up more. Keeping the car tilted forward means that you will not need to drain the transmission. The rear bumper should be at least an extra foot higher than it was to get a good enough angle. This will save some time.
Ok, then the second little trick to saving a lot of time, not having to actually remove the transmission tail housing from the car. The key to this is being able to remove the transmission mount without taking the cross member out. You can try to go at it by unbolting it and jacking the transmission up into the bottom of the car, but even then it will be a good 20 minute battle to get it out. OR, you can use the image below and cut the studs off at the bolts. Do this with the nuts on so that when you remove the nuts they straiten out the threads. The excess bolt length will never be needed so cutting it will not in any way effect anything negatively. Then remove the two bolts holding the mount on to the transmission tail housing.
Now remove the drive shaft. The bolts that hold the driveshaft to the pinion flange are 12mm 12 point bolt heads. So you will need a 12mm 12 point socket, do not try to use anything but a 12mm 12 point socket. The torque on them is pretty high, so anything else will stand a good change of stripping the head or breaking. (Note the drive shaft bolts have a 75-90ft*lb torque spec)
Now go back to that cross member, and remove the bolt/nut at each end that secure it to the frame. Do not remove the cross member.
Now, put the transmission in neutral. Get a piece of plywood and put that on the car jack, and jack up the transmission from the fluid pan, the plywood should be large enough so you don't damage the pan. Jack the tranny up into the floor board, you will feel some resistance, but there is nothing damageable on top the transmission, but keep in mind that jack you are using can exert a good 2-4 tons of force. You are just getting some room so you can pull that transmission mount out.
Once you have the mount out, you can put a car stand below the transmission to hold it up, but you can just use the car jack for now. Even if the jack fails it will not drop far because you LEFT THE CROSS MEMBER IN. Use the jack to lower the trans back to its normal position (with the mount still removed).
Now remove the 6 bolts that hold the tail housing onto the transmission (1/2" bolts). Once they are removed pull the housing off the transmission body, try to make sure the gasket doesn't get damaged. It may be stuck on, so don't be afraid to get a little leverage somewhere. IF you damage the gasket when you pull the housing back, then you will need to remover that cross member and take the tail shaft housing off to replace it with a new one. You can do this anyways if you want to, but it's not a high pressure seal so it usually does just fine.
Withe the transmission in neutral, you can turn the governor so that you can see the two phillips head screws. As in the last pic. If you go to turn it and it wont turn then it's probably just not in neutral. If you have the transmission above or below it's normal position the linkage may cause it to be in a different gear than the indicator says. Just get it to a point where you can turn it. Then put it back in Park so it doesn't go moving on you when you go to remove the screws.
PLEASE, make sure the two screws on the side are pointing towards the front. If you put it on backwards it will hit the inside of the housing and who knows what will happen with a bunch of aluminum shreds floating around there. Tighten the governor screws down 'good and tight'....what ever that means. Don't go crazy on them, but get them tight. Everything except the drive shaft bolts just needs to be tightened till they are tight, not specs. Just revers everything to put it back together, and that is that. (Note the drive shaft bolts have a 75-90ft*lb torque spec)