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To really get the carburetor clean inside and out you will need to soak it in carburetor cleaner. You can purchase a 1 gallon can/kit from most any auto parts store. The can has a metal basket inside that you can put the smaller bits and pieces in to soak them too. The cans now a days are not labeled as carburetor cleaner but as parts cleaner. You will need to repaint your carburetor after soaking it as the paint will be removed.
Scrub it with soap and water afterwards and blow out the passages with compressed air. I like to heat my carbs with a propane torch right after washing and blowing them out to reduce rust flash over and to get the passages nice and dry.
Don't be in too much of a rush to use the needle valve that comes in the kit if the tip on yours is still in good shape. I've never been terribly impressed with the fit of the new ones.
The kit works really well for cleaning up other parts just be sure to wear nitrile gloves as it will take the oils out of your skin pretty darn quick.