If a concrete slab is directly under tree limbs, or has an accumulation of leaves on top of it for a time, it can be stained by the tannin in the leaves. Removing those stains can be done in an afternoon, and usually will not require the use of harsh chemicals. In some extreme circumstances, you may have to use a masonry cleaner such as muriatic acid, but ordinary soap and bleach will work most of the time.
Fill the bucket halfway with water, and stir in one cup bleach. Add 1/4-cup laundry soap, and stir the mixture well. Pour a small amount of the mixture directly on the stains, and work it in well with the broom.
Sprinkle a thin coating of laundry soap over the wet area, and work it vigorously with the broom for three minutes. Allow the mixture to set for 15 minutes. This allows the bleach to soak into the tiny cracks and crevices in the concrete.
Wet the area with your bleach mixture again, and scrub it with the broom. Rinse the area well with a garden hose. This method will work for most common stains, including many types of grease and oil. Bleach is not effective at cutting oil, but washing powder is formulated to remove oil and grime.
For worked in oil, grime or rust stains, you may need to resort to methods that are a bit more harsh. For this, you will need to purchase a masonry cleaner that contains muriatic acid. You can purchase the acid at "full strength," but keep in mind it is extremely dangerous to work with, and wear gloves and eye protection.
Pour a small amount of the acid directly on the stain. Hold the container near the ground to avoid splashes or splatters from the acid. Only apply it to a small area at a time, and be careful not to step on the area as it will cause soft-soled shoes to deteriorate.
Work the acid into the area with the broom. Again, be careful not to splash the chemical onto your skin or clothing as it can cause painful burns. Allow the area to stand for 15 minutes.
Rinse the area thoroughly with a garden hose. Remember, only use a small amount at a time, and rinse each section well before moving on to the next. This allows a higher dilution of the concrete cleaner as it is washed away, eliminating the danger posed by the "full strength" formula.
Bleach is one of the best all-purpose cleaners you will find. It also is considered environmentally safe by the Environmental Protection Agency. Anytime you are working with items that could splash or get blown into your eyes, take an extra moment to put on a pair of safety glasses.
Do not mix muriatic acid with bleach or other chemicals. Muriatic acid can be dangerous. It produces a chemical reaction on the concrete that creates intense fumes, so be sure to provide adequate ventilation if you must use it.