Changing the muffler on your vehicle is not a very technical job, but can be a physically strenuous project to tackle considering how long the muffler has been on the car. This is a job that will save you a lot of money if you decide to do it yourself.
If your vehicle is low to the ground keeping you from reaching the muffler it will need to be parked on ramps or jacked up and placed on jack stands. After you have successfully jacked up the car or placed it on ramps you will need to check where the muffler is connect by mounting brackets and the pipes that fit into the front and rear of the muffler. Make a note of the nut and bolt sizes you will need to remove and the wrench types that are going to be best for the job and gather all the tools for the job so you will not have to make many trips out from under the vehicle. These nuts and bolts have probably spent years under the car in all weather conditions and may be ceased up. To help with these you may want to spray them with penetrating oil and let them set for a while before attempting to remove them. Some other tools you may need are a hammer, pry bar, and a light source such as a drop light. Make sure to wear safety glasses because you will be working on your back looking up and all the dirt that gets knocked loose from the car while working on it will be falling toward you. A good pair of mechanics gloves may help as well.
Now that you have gathered tools and made any other preparations you are ready to start removing the muffler. Loosen the clamps that are holding the exhaust pipes to the muffler and if possible completely remove them. Now that the clamps are lose you can remove the bolts from any mounting bracket that is on the muffler. In some cases the brackets will be on the exhaust pipe. If this is the case remove them as well. The clamps are loose and the mounting brackets are removed so it is time to start working the muffler off by pulling it towards the back of the vehicle. The area around the insert for the exhaust pipe may need some penetrating oil to help free the connection. If you are having trouble tap the front of the muffler with hammer or find a solid place to pry from. Pulling and tapping or prying at the same time should cause the muffler to begin sliding off the exhaust pipe and after a while you should be able to work the muffler completely of the exhaust pipe.
The new muffler will go on reversing the steps from the removal of the old muffler. Clean the ends of the exhaust pipes that fit into the muffler with a wire brush and apply a coat of anti-cease if possible to help everything slide together with ease. It may be a good idea to replace the clamps and other fasteners such as nuts and bolts at this time. These items have been under the car for who knows how long and may be close to failing. After everything has been replaced lower the car from the ramps or jacks and start the engine so you can listen for exhaust leaks. If your vehicle has no exhaust leaks you have successfully replaced the muffler.