Before sweeping a large concrete floor or patio, sprinkle slightly damp coffee grounds on the surface. They will keep the dust down and pick up the dirt.
To get dried raw egg off a concrete floor, scrub the egg with a scrub brush while pouring on boiling water.Wear heavy rubber gloves for this process and be very careful to avoid burning yourself.

To clean grease and oil from a concrete floor, sprinkle TSP (or other product containing trisodium phosphate) over the area, add a little hot water to make a thin paste and scrub vigorously with a stiff bristle brush. Allow the paste to sit for 20 minutes, then rinse with water. Repeat the process if necessary.

If the oil spill on a concrete floor is a small one, you can treat it by covering it with a prewash spray designed for fabric stains. Let the cleaner sit for a few minutes, then sprinkle on a cleanser such as Comet. Scrub with a stiff brush or broom, then rinse with the hose. Oil on concrete can also be removed by soaking the stain with paint thinner for 20 minutes or so.

If any residual stain is left on your concrete floor after one of the above approaches, you can get out the last of it with a solution of 1 cup of laundry detergent, 1 cup of household (5%) bleach and 1 gallon of cold water. Be sure the concrete is dry, then scrub the solution into the stain. When the stain is gone, rinse off the solution with the hose.