Ha. Fairly clean? I wish somebody had told my clients that when I was still working! If you hire a service, they are there to clean...you don't have to clean before they get there.
If you're going to do it yourself, start at the top. Work down. A long-handled duster (or a broom with a rag tied around it) will do to dust down cobwebs and dust ceiling fan blades. Dust one entire side of the room, including picture frames, at a time, then move on to the next wall until all four have been done. Dust the furniture and doo-dads, then the baseboards.
Use a crevice tool on the wand for your vacuum to reach as far as you can under heavy furniture.
When you vacuum, start at the point farthest away from the door and vacuum your way out of the room.
Dust in the bathroom first. Then clean the mirror, vanity and sink, and obviously, clean the toilet last.
Dust in the kitchen. Wipe down the outside of the cabinets and the appliances. Clean the countertops and the sink.
Use a dust mop or a Swiffer on floors that aren't carpeted. Wash the floors. Et voila! Done.
And...if you have stainless steel appliances and/or a stainless steel sink, don't spend money on stainless steel polish. Spray some furniture polish on a clean cloth and wipe the appliances in the same direction as the "grain" of the finish.
If you have a two-story house, instead of trying to drag a vacuum down the stairs while vacuuming, use a whisk broom.
As far as I know, it's not carved in stone that you have to clean the whole house at once, just remember to start at the top.