Pour a cup of each color paint into a bucket -- each one into its own bucket. Add about three gallons of water to each bucket and mix to dilute the paint.
Dip the sponge in the light green paint water and squeeze it over the surface of the concrete walkway. Use the push broom to spread the paint-water solution around.
Squeeze the dark green paint water over the surface of the concrete walkway. Do this in a manner that allows the dark green water to puddle mildly; distribute it unevenly to get a natural look.
Repeat Step 3 for both the black paint water and the brown paint water. Try to avoid puddling too many colors over each other. The surface of the walkway should be covered in a random pattern with no consistencies.
Let the walkway dry for a week and do not allow anyone to walk over it. This will allow the aged look to settle in. Use a sponge to apply concrete sealant to protect your color. Let the sealant dry.