Post edit: The first point to check, especially when you have just acquired the machine, is the spark plug. Two stroke spark plugs do not last very long anyway, but if the previous owner let it idle for substantial periods, the plug life might be very, very short. Try a new plug of the correct type. Don't throw the old one away: if the new one makes no difference, put the original one back in and keep the new one for next time.
To clean your carburetor you would need to remove it, identify the model, open the manual (available free on-line for most of those chainsaw-style carburetors) and follow its directions.
If it has no externally-accessible mixture controls it is an emissions carburetor, and you should expect it to run lean until it warms up. My system is to leave the choke partly on, and gradually open it as warm-up progresses.
