Sweep the slab's surface to remove all loose particles. Scrub the concrete with concrete cleaner, then rinse the slab with fresh water.
Install 2-inch-by-8-inch form boards along any open slab edges to contain the new concrete. Place the tops of the form boards at least 1/2 inch above the surface of the concrete. Extend them farther if a thicker overlay or a higher concrete floor is desired. Secure the boards with stakes, rocks or concrete screws.
Measure and make several marks the same distance up from the concrete slab on any walls adjacent to the slab. Snap a chalk line through the marks to make a straight line indicating where the surface of the overlay will sit.
Paint the surface of the slab with a concrete bonding agent.
Pour fresh concrete onto the slab, up to the tops of the form boards and the marked lines on the walls. Roughly level the concrete at the top with a 2-inch-by-4-inch board.
Smooth the surface further with a concrete float. Skate the float back and forth across the surface of the overlay in an arcing pattern.
Mist the overlay evenly with concrete curing agent. Allow the concrete to fully cure. Mist the surface of the overlay periodically to prevent the concrete from curing too quickly. Cover the concrete with plastic while it cures if the ambient environment is dry.