I hate dust sheets with a passion! Had more trips and slips with them than anything else, give me a nice safe power saw or ladder anytime!
That dust sheet on a tiled floor is an accident waiting to happen.
You can get rubberised dust sheets which will grip smooth floors, but they are no good for pile carpet as they "walk"I use the disposable plastic sheet on cabinets etc it can be heald in place with masking tape and lifted up and laid on top of the cabinets overnight cardboard taped to worktops works well. Standard dust sheets on carpet can be taped in position.
As for clearing up fold with the rubbish inside then tip it out onto a easily cleaned surface vinyl or outside on concrete then vacuum it up and shake the dust sheet outside, my dust sheets were washed at least once a week.
With a tradesman he cannot dust sheet cards, vases, and plants they should be cleared away before he arrives.
Firstly you should clear everything from the worktops, take down blinds etc, then your sheets can be held in place with tape stuck to the tiles. As for cleaning them, I use a launderette where they have bigger machines, ok for standard cotton twill sheets but not for laminated, poly backed sheets.
In a room like that I would use polythene dust sheets to cover the units. They weigh very little and don't need heavy objects to hold them in place. You can buy rolls of poly and cut them to length. They are so cheap that you can bin them each day if you want.
As others have suggested, the worktops should be clutter free.
Toolstation sell cheap tarpaulins which you can use on the floor if you want. Alternatively You could use a roll and stroll adhesive film to cover the floor tiles if they will be inplace for a prolonged period (much more expensive though).
I'm with opps on this - poly dust sheets are the modern way - I sheeted a whole room when I painted just the ceiling.Attach plastic sheet with low tack masking tape. No way I would go back to Twill ones like my old dad used, though they're so strong they'll last many years more. (folded and stored for now)
How you can work in that kitchen with all that junk on the worktops and draining board and the floor is beyond me. As for painting the ceiling, which I appreciate you are not doing, I have just bought one of those Paint Runner roller doobries. No splashes, no drips, no dust sheets. Worked for me although it does take a bit to get it going initially.