I use a small torch to heat up the jets and emulsifier tube and burn the goo out, then hit them with a bit of brake parts cleaner.I work on small engines and if it is a Briggs engine, some of their carbs have 3 holes in the plug at the bottom of the carb. I use OxyAccet torch tip cleaners and clean those holes out. The biggest thing I can recommend is to only use Non-Ethanol Gas in those small engines if they sit for a while. If you are going to use it for a while and go thru lots of gas then Ethanol will work as long as you drain it out when you get done at the end of they season and then refill with Non-Ethanol and allow it to run a min or two. Carbs can be really tricky and a pain in the backside!
Sometimes a little poke with a piece of wire is needed, but not normally.
Last week I did one on a lawn mower for a friend. The inside of the carb was as clean as the last time I had done it 2 yrs ago, all I did was pulled it apart and put it back together and it ran great. On this particular carb the fuel bowl is filled thru the bowl bolt, so care must be taken to align it with the slot on the carb. I used a sharpie to mark the bolt, then you align the mark on the bolt with the fuel inlet. It's easy to do, but I bet many have over-tightened the bolt causing less or no fuel to get into the bowl and thus creating a no run or a situation where it only runs for a short period as the bowl will not fill quick enough to keep the engine running.