Once you’ve got the kitchen and bathroom surfaces in hand, you can start on their floors. A vacuum cleaner-broom combo works best for any dry floor including kitchen and bathroom.

Put your hand (wearing thin disposable gloves,) on the kitchen floor in a few places to check the dirt level especially under appliances and fixtures. Sweep out these areas. (This is generally easier than taking attachments on and off the vacuum.) Vacuum cleaners aren’t so good in tight corners but are excellent when you can’t see those dust bunnies hopping.

Vacuum around the walls to get all those bits. Now you have a clean margin. Pick a spot with your back or hip against a wall. (Standing in the center risks missing some dust even if you see quite well.) Vacuum the area in front of you with over-lapping strokes then side-step a couple of feet and vacuum the next strip until you reach the far wall.

Mopping is much the same. Use a soapy rag under fixtures, in corners and on baseboard. (You can attach the cloth to a Swifer-mop if getting down to the job is tricky. Then use your mop in over-lapping stroked for the center of the room.

If the room is large, vacuum in strips using a stool to mark the strip edge. Of course you sometimes have to vacuum under things, but return to your pattern afterwards.

Cleaning up after a breakage:

First find a way to mark the spot such as putting a chair or stool over the broken glass or crockery. Then shut out pets and put on shoes yourself. Find thick work gloves (not rubber gloves). Double-bag paper shopping bags and, wearing the gloves, gently find the big pieces and lift them into it. Now get a sweeping broom and dustpan. Sweep up all the little pieces. (On a hard floor you can hear them.) Vacuum as well. Fold the paper bags so the broken crockery is well-enclosed.

If you have broken something with jelly or liquid inside you might have to sacrifice an old towel. Wearing the thick gloves drop the towel over the whole mess and broken bits and gently scoop it all into the paper bags. You will still have to check the area carefully of course and probably use a mop and paper towel. Using a tray to prepare food and drink is the best way to prevent breakages.