I'm sure there are better ways, but this is what I do:
1. Completely disassemble
2. Clean each small piece with a can of carb cleaner and a stiff bristle brush (use the carb bowl to hold the pieces and collect the carb cleaner)
3. If really bad, let them soak in the bowl overnight
4. Clean carb body with the brush and carb cleaner, make sure every passage is clean and easy to blow through
5. Replace pilot, main, and power jet
6. Replace needle and seat if worn, or questionable
7. Reassemble.