The Chevy Blazer has its muffler near the rear of the truck with just a short tailpipe section on the end of the muffler. The muffler can be replaced with a new OE muffler or an aftermarket unit from any one of several auto parts stores. The muffler is a single inlet/single outlet unit. The mount used to hold it in place is a removable band that wraps around the muffler and has the mounting rods on the top to connect to the rubber mounts on the frame.
Raise the rear of your Blazer off the ground with a jack. Support the truck with a set of jack stands positioned under the frame rails, making sure it is stable.
Raise the muffler up under the frame mounts for the muffler, slide the rubber isolator/mounts over the mounting rods, then lift the front of the muffler and align it with the exhaust pipe. Push the muffler and exhaust pipe together, then install a new exhaust clamp onto the pipe and tighten the nuts with a socket and ratchet.
Slide the tailpipe onto the outlet side of the muffler and install a new exhaust clamp. Tighten the nuts on the clamp with a socket and ratchet, being careful not to overtighten the nuts or you will crush the pipe.
Inspect the exhaust hangers and clamps on the rest of the system while you are under the truck and replace any that are rusted or have damage of some kind.
Raise the truck off the jack stands with the jack, remove the stands from under the truck and lower the jack. Test-run the engine to ensure you do not have excessive noise or any obvious leaks in the system.