Start by removing the spark plug.
Next remove the muffler.
Pay close attention how it comes off. They often have small pieces ( Baffles and such ) that will come off with the muffler. If the muffler will open... Open it up and see if it is full of carbon. Remove any and all carbon.
You can burn the carbon out with a propain torch if you have to.
Before replacing the muffler look into the exhaust port.
Pull the rope and watch as the piston rises and falls. Look for scratches and grooves on the piston.
If you can see over the top of the piston look at the cylinder walls as well. You may need to shine a flashlight
threw the sparkplug hole to see into the cylinder.
If you see very many scratches the saw is toast and will need to be replaced.
If the piston and cylinder look good... Replace the cleaned out muffler and install a NEW spark plug.
Clean the air filter. You can, for a very short time, test run the saw with out the air filter.
Start the saw. If it DOES NOT run right turn it off. It will , most likely, need a new carburetor and fuel lines.
If is is sucking air threw a cracked fuel line.... Running it that way will ruin the moter
This is something that you can do.....
David