When I first started turning, I cleaned up after every session.  Then I got lazy.  Today, I let shavings and dust accumulate until I can no longer stand the disorder.   

I keep an old plastic garbage can in the shop that serves as a stand/holder for a plastic bin liner.  So once a month (or thereabouts),  I will sweep up the shavings and stash them in the plastic bin liner.  I also use that as a place to dispose of the waste from the paper shredder in my office, and when it gets full, it goes out with the garbage.

I typically use either paper towel or toilet paper to apply finish, and when I am done, I drape the oily paper over the edge of the bin liner for a few days until the oil cures before tipping it over into the shavings and shredded paper.   

But there are some areas in my shop that aren't touched in that ordinary cleaning routine - under/behind the lathe stand, for example.  So every couple of years I get out the shop vac and do a thorough cleaning.  Seem to turn up a few dead mice whenever I do that.

Depends.  If I'm doing something like a batch of rolling pins where I get little chips of wood, at the end of the day I'll just sweep everything into a pile under the lathe.  If I'm roughing a batch of bowls, then I'll usually scoop up the majority of the shavings at the end of the day. (keeps rust down once I had the leveling bolts on the lathe start rusting from being covered in wet shavings).

just hauled off two 30 gal. cans full of curlies and a 15 gal barrel from the dust collector and no i didn't sweep maybe later.  does that help answer your question?

David I know what you mean.  I have a couple of plastic trash cans I put cut offs in.  But the chunks from rounding bowl blanks are a pain.  They don't even stack nicely on the firewood stacks.