Whenever I try to knead (by hand) or move after kneading, a high hydration dough like ciabatta, it sticks to my hands terribly and often seems ruin any shaping I try. I've tried flour on my hands, but it comes off so quick - what can I do to keep it from sticking so badly?
Let the dough rest in the bowl for a while after mixing. Time will not only improve the flavor (insert autolyse proselytism here) but will also give the flour time to hydrate, making the dough somewhat easier to handle.
Dough will become less sticky as you work it -- witness the way dough kneaded in a mixer or food processor initially sticks to the sides but eventually forms a ball and leaves the bowl clean. So, one option is to work it a bit with a mixer first, or just with a wooden spoon in the bowl.
Anil's suggestion to oil your hands is a good one. If the kind of dough you're making allows it, add some oil or butter to the dough during mixing, too.
Flour helps, of course. Instead of trying to coat your hands in flour, throw a bit on the kneading surface and on the top of the dough.
For very sticky dough, a dough knife can help you scrape the dough off the surface and fold it over onto itself until it becomes easier to handle. This is easiest if you're working on a hard, smooth kneading surface like marble.
My suggestion is to try it with grease or oil, similar to oiling utensils. This is what you can do when you prepare dough. If you are concerned about the amount of oil in the bread, you can try flour.
Apart from this, the dough consistency plays a major role. If you make your dough a little harder, the stickiness will decrease. If it is too loose, it will stick a lot.
There are two main ways this is accomplished, and one condition which will cause stickiness.
To mitigate sticking:
I usually knead by hand, and keeping my hands generously moist is often enough to prevent sticking (I knead in a bowl). This causes the dough to be a little wetter than I aim for.
Then, while shaping, I will use flour on the surface, since I won't be knead it anymore.
I will put some oil on the baking parchment when baking, to prevent sticking.
What causes dough to stick overly much is not sufficient hydration (time) and gluten formation (time & kneading)