How do I deal with a really wet, messy dough?
For very high hydration loaves, you want to create your gluten development without adding an excess of flour which would reduce the relative hydration.

This video from Italyum Recipes shows the classic stretch, slap and fold method, using a 70% hydration dough.  Basically, you lift the entire dough from the work surface, allow it to stretch under its own weight, then slam it down again.  Rinse and repeat.

A somewhat less labor instensive method is described at The Fresh Loaf (the article has a lot of introductory material, keep reading and there are really clear instructions with lots of photos):


Initially stir the dough together until it is is a thick and cohesive liquid, which the author describes as "like porridge."
Use the stretch and fold method of kneading to create some development:


Flour your work surface moderately
Pour the dough out onto the surface
Use your bench knife knife (also called a dough scraper) to lift and drop the dough back on itself, stretching it. See this image from the Fresh Loaf:



Allow the dough to rest and autolyse, that is, develop gluten from the reaction of the water and precursor proteins in the presence of enzymes naturally in the flour.   This limits the amount of hand kneading you have to do.
Repeat the stretch and fold method a couple of times to get the final development


Finally, note that very wet doughs can also be kneaded entirely in a stand mixer simply by beating them for a couple of minutes.   These doughs are wet enough to be nearly pourable, and do not climb and clump onto the paddle; if they do, the hydration is not high enough for this method, and you need to use the dough hook instead.