Cleaning the kitchen floor doesn't have to be hard. Here's an easy four step plan to clean your kitchen floor. I call it sweep, scrub, scrape, rinse - a very not original name.
1. Sweep - using a broom, sweep away the loose dirt, food droppings, dust, etc.
2. Scrub - scrub the floor with your natural cleaning product
3. Scrape - scrape away the dirty water/cleaner you've left behind
4. Rinse - go over the floor with a final rinse of clean water
While you're cleaning the kitchen floor, you may want to turn on all available lights so that you can see the floor better.
You may think of just doing the floor in one go. If you do that, you'll just move the dirt around instead of cleaning the kitchen floor.