to start te TRD muffler is an axle back, meaning its components start at the rear axle and go back... obvious..... now the first thing obviousl is to jack up the car on both sides, then use jack stands to help keep the car stable... NEVER trust the jacks, ALWAYS use jack stands.. (something that takes extra time and is a side step could be to remove both rear tires and slide them under the car and position them, so if the car was to fall the tires would catch it, but this is just a side step)
so remove the bolts that hook the muffler to the mid pipe, which is around the rear axle area first, then around varius locations there are rubber "doughnuts" that need to be removed carefully with something like a crowbar, and very carefully cuz they need to be reused. pull out the muffler and throw it aside, sav it if you plan to sell the vehicle in the future cuz some people prefer stock parts... then with a buddy prepare the mounting of the TRD muffler and, your buddy holding the TRD muffler up, reinstall the rubber "doughnuts" let it hang and get it positioned properly and when it is fit properly start putting the bolts back on but dont fully tighten them until they are all on, then go back and tighten them all....
shouldnt be to hard.. you can use rubber gloves to do it if you want so you dont leave fingure prints.. if not be sure to clean the muffler with rubbing alcohole to remove the greasy finger prints or else the heat will burn them on... you ma need to use penetrting oil on the bolts if its a 04-07 model, cuz its been used constanty and heat has gotten to it so the bolts may be "burned" on by the heat.......
plan B, as a back up, call Toyota and set up an appointment to get them to install it.
05 Scion tC owner.