The basics of carb clening are pulling off the carb and dismantling.
Spray carb cleaner, kerosene bath, or comercial carb baths are the norm.
A tooth brush, and, small flat screwdriver helps in scraping crud off, thin wire helps to clean out corroded and gummed up passages and compressed air or carb cleaner spray with the straw attached help determine if the passage in question is clear. Needle valves can go bad, but dirt and old gas are the usual suspects. The needle should have @ 45 degree angle on it where it meets the seat. Often times the numbers on the carb and a google.search will reveal a carb rebuild kit (if needed) and a few YouTube videos will make you an old pro at rebuilding small engine carburetors.