A carburetor does two basic things: it delivers air and it delivers fuel to the engine’s combustion chamber. Air and fuel in the proper combination are essential to engine performance. If either of these pathways—that of the air or fuel—is obstructed or impeded, the carburetor will not work at peak efficiency.
Suction generated by the engine’s piston when on its down-stroke draws air in through the carburetor’s throat. Situated in the pathway between the outside air and the carburetor’s throat is an air filter. Sometimes the carburetor is actually clean enough to be in good working order but the air filter is clogged. In this case, simply cleaning or replacing the air filter can make a big difference. Once the air filter is ruled out as the culprit, an aerosol spray cleaner formulated especially for carburetors can be used and will generally do a good job of cleaning the carburetor’s air intake components.
No amount of cleaning of the air intake components will help if the problem is in the fuel components. Deposits and impurities can gum up needle valves and interfere with fuel passage. In this case, a fuel additive designed to dissolve these deposits can help.
Once the fuel additive is mixed in the fuel tank, it may take a number of pulls of the starting cord to get enough of the solvent to pass into and through the needle valves to do its work. Even if the engine is not starting right away, the cleaning agents should still be passing through the carburetor with each pull of the cord. Several cord-pulls, a period of rest, several more cord-pulls, then another period of rest may result in enough cleaner getting into the valves to eventually free up the passages and allow the saw to run properly.
If the carburetor has more stubborn cleaning needs than can be addressed with off-the-shelf fuel and air intake cleaners, it may be necessary to remove the carburetor from the engine, disassemble it and clean it in a parts cleaner with special solvents. Unless the owner has the equipment and experience to take on this task, it's a job best suited to a shop that specializes in working on small engines.