How to clean up after kneading dough?
Kneading in a bowl is time-consuming and doesn't give as good a result as kneading on a flat surface, however I'll concentrate on cleaning. 

First, don't let things dry out, it's much easier to clean when things are moist, if you do let it dry out moisten it and let it soften before you try and clean it. Use cold water as hot water makes starches and proteins stick a lot more. Next, invest in a curved dough scraper, and use it to scrape out the dough scraps from the bowl into the garbage before you clean it. A curved plastic one works best as it has a bit of flex, although in a pinch you can use a big metal spoon. I scrape by bowl pretty much clean before I put it into the sink. Use the flat of the scraper to clear most of the dough and flour from your countertop, then spray down with water, let it soak for a few minutes, then scrape again. Once you have it scraped well sponge it down.