Write an article based on this "Spray rust penetrator on the exhaust clamps. Loosen the exhaust clamps with a wrench. Slide the exhaust and muffler apart. Hang the new muffler on the mounts. Spray exhaust sealant on the ends of both pipes. Slide the exhaust pipes together. Secure the muffler clamps onto the pipe."
If your muffler is not welded in place, it will be secured using muffler clamps.  Spray a rust penetrator like WD40 onto the fastening hardware to break through some of the rust and grime that may have seized the nuts in place.  You may need to spray the bolts and let them sit a few times before they are able to be loosened. You can purchase rust penetrator at most auto parts or large retail stores. Once the fasteners have been thoroughly soaked in rust penetrator, use a wrench to remove the nuts holding the exhaust clamp in place.  Make sure to use a socket or wrench of the correct size, as exhaust fasteners are prone to stripping or breaking.  If you intend to reuse the muffler clamp, you may want to spray it with more rust penetrator as you work it loose. You can purchase replacement muffler clamps at most auto parts stores if they are too rusty to be reused. Because the muffler and the piping have been held together with the exhaust clamp for so long, they may not come apart easily once the clamp is removed.  Spray some rust penetrator where the two pipes meet and try to work them away from one another until they slide completely apart.  If the pipes are rusted together, you may have to cut the pipes apart. If your muffler was welded in place, you will have to cut the pipes apart. The muffler will have metal prongs sticking out of the top that slide into rubber eyelets below the body of the car.  You may have to push the prongs through the rubber with a bit of force to get past the initial ridge.  The rubber will prevent the muffler from rattling inside the cabin of the vehicle once the muffler is completely installed. There should still be enough play in the rubber mounts to allow you to move the muffler around as you connect it to the exhaust pipe. Spray exhaust sealant on the pipe coming from the exhaust and the pipe it will connect to on the muffler.  This will help establish a seal between the pipes and prevent any exhaust from leaking at the joint.  Refer to the instructions on the exhaust sealant to know how long to let it cure. You can purchase exhaust sealant at your local auto parts store. Slide the pipe from the muffler over the existing exhaust pipe.  The muffler should rest directly below the rubber eyelets its mounted to, so the eyelet should hang straight up and down when the pipes are joined properly.  If the two pipes feel loose or can be wiggled, you will need an adaptor to match the correct size.  Most exhaust piping comes in two or two-and-a-half-inch diameters. You will not be able to seal the wrong size pipe onto another pipe, but adaptors for most diameters can be purchased at hardware or auto parts stores. With the piping seated properly, slide a muffler clamp over the area where the muffler pipe overlaps the other.  Use a hand or socket wrench to tighten the clamp until it is not possible to move the pipes back and forth at all.  You may want to use a half inch drive wrench to tighten the clamps to make sure you have enough leverage to tighten it sufficiently. Be sure you tighten the clamp where the piping overlaps, otherwise you may not create a solid seal.