I power wash.
Pressure washing is probably the best. You can rent them for a day or weekend, but you can now buy them to attach to the hose. Check at your home improvement stores.
Start with broom and dishwashing soap...the pressure wash. Later on seal it.
For a lightly soiled patio, you can remove dirt with a cleaner and a stiff brush. You can use bleach mixed with water. Add 1/8 cup of liquid dish washing detergent to the solution and put into a spray bottle. Spray the solution onto the surface, let sit for a few minutes and then scrub with a stiff nylon-bristled brush.
We are power washing on concrete driveway, it an amazing change.