To make this work, you need to have cleaning supplies at hand. I make 'green' cleaning products with water, vinegar, borax, olive oil-based liquid soaps, and essential oils for fragrance. They are stored in clear spray bottles under my kitchen and bathroom sinks so I don't have to go far, and re-fills are easy. Bring out your dust cloths, vacuum, and other cleaning equipment, so everything is within reach before you start. Start with the main rooms. If you’re having guests and you’re trying to clean before they arrive, concentrate on the rooms they are most likely to see such as the living room, the kitchen and the bathroom. Leave bedrooms and other rooms until the end and clean them only if time allows.
1. Start in one corner of the room, and move in a circle around the room. Pick up any items on the floor, from tables, counters, and chairs as you walk along, and anything out of place. For large or joined rooms - like a kitchen/family room combination - divide the room into squares and complete everything in one square before you move on.
2. Put things away as you move around the room or - if they belong elsewhere - place things into a laundry basket or fabric tote. Fortunately, toys don't have far to go since I have some storage in every room. I load them and then can easily carry clothes and shoes to the bedrooms, or mail and newspapers to the office area. 
3. As I walk and pick up, I carry my solutions to spray. My dusting solution is Murphy's oil and my counter cleaners require no scrubbing. Wood sprays don't get used unless there are messy fingerprints - I have a small "Magic Duster" that I swipe accessories, lamps, tables and wooden chairs with. Start with the right cleaner for the surface, spritz on and move on to clean somewhere else while you wait a few minutes for it to work. This is great for greasy counters, scuff marks on floors, and letting cleaners work on grout. For living rooms you may just need to dust, but this helps if you have to wipe a window, glass display items, and non-wood surfaces.4. Go back and wipe up all of your sprays. I use old washcloths or dishtowels instead of paper towels and I use several in one room so the counter one doesn't get used to wipe appliances, or dust tables, or clean mirrors and windows.
5. Dust, starting with anything that is dark wood, as dust shows more clearly on dark surfaces. Here is where that Magic Duster comes in handy. The fibers attract dust, and I can do one whole room without cleaning the duster. Don’t use a dry rag since you don't want dust from flying around the room as you clean. Some Swiffer products work well, but their disposable nature is costly and an environmental disaster since they are not recyclable. Again, old towels, diapers, dishrags and underwear work well and can be washed with regular laundry as needed.
7.Next is to vacuum. Nothing will give a better impression of a clean room than freshly-vacuumed rugs. I have area rugs in every space so I do the wood floor and the rug at the same time. You can use a fragranced vacuum powder to improve the overall air smell of the room as you clean. Don’t bother vacuuming curtains but DO remove pet hair from the upholstery.
8. Spray a bit of room spray in the air - something seasonal is great - and voila, you are finished!