Spray the surface of the concrete you will be repairing, using a pressure washer. The entire surface of the concrete needs to be wet. Start on one side of the concrete slab and work across it to effectively remove the dirt.
Pour a masonry cleaning solution into the pressure washer. Spray the solution over the entire surface of the concrete. Flush out the pressure washer with clean water when you are done to remove the leftover solution from the system.
Rinse away the cleaning solution with a high-pressure tip attached to the wand of your pressure washer. Hold the tip a few inches away from the surface of the concrete. Take your time with this step to remove as much dirt and mildew as possible.
Pour concrete patching compound into a large bucket. Add the amount of water recommended by the manufacturer. Mix the water and patching compound with a piece of scrap wood or an electric mixing paddle.
Pour the mixture out of the bucket and into the crack. Push the patching compound into the crack with the edge of a flat trowel. Lay the trowel across the top of the crack. Slowly drag it backward to scrape the excess compound off the surface of the concrete.
Lay a piece of plastic sheeting over the patched area. Hold the edges of the plastic sheeting down with bricks to prevent it from blowing away. Keep the patched area covered for 5 days. Lift the plastic and moisten the area with water once per day.