Which nut are you talking about? On these year mustangs you take apart the rear brakes down to taking the rotors off. Then you take off the diff cover, the bolt holding the pin in the diff center section. Then you take the pin out, pull the c-clips and pull the axles out. At that point you remove the rear axle seals and use a slide hammer to take the rear bearings out. You have to hammer the new bearings in and then you can reverse the procedure making sure you dont get grease on the brake pads or rotors. Make sure to refill the diff when you are done.
As far as fastener sizes, its been a bit since I have done one. You will want a fairly complete set of metric and standard size sockets with associated ratchets and wrenches to your brand preference.
bdcardinal's description of the process still applies: remove the axle as described, pop the seal out and use a slide-hammer to yank the bearing out.
There is no one "nut" to this process. It's not like the front wheel hub assembly that really is retained by a giant 36mm nut torqued to 260 ft-lbs. More work is required to get to the rear axle bearing...
Edit: You are talking about a solid-axle assembly and not an IRS, right?