Wear protective clothing that covers as much exposed skin as possible. Long pants and a long-sleeved shirt along with work boots, safety goggles, a hat and a respirator to protect you from the harmful dust kicked up with the grinding process should provide you with sufficient protection.
Grind the surface of the patio. Place a 32-grit diamond pad on a concrete polishing machine that you can rent from an equipment rental shop or home improvement store. Run the polisher over the entire surface of the concrete, working in small circles and grinding down the surface of the patio to level any high spots. This pass will leave the concrete surface with tiny air holes from air pockets created when the slab was poured. Spray a thin layer of acrylic tile adhesive onto the patio to hold the dust created with the first polishing pass, filling in the air holes in the concrete surface. Allow the adhesive to dry for two hours.
Remove surface imperfections and complete the leveling by changing the diamond pad to a 60-grit pad and repeating the grinding. This pass will remove the most glaring imperfections, such as rough edges. Spray a layer of reactive concrete hardener onto the patio to harden the surface. A harder surface will create a more brilliant shine. Change to a 120-grit pad and grind the surface a final time to completely level it.
Spray a layer of concrete stain to the surface of the patio to add color to the concrete. Apply the stain starting at the corner of the patio, and spreading it evenly across the patio's surface. Allow the stain to dry according to the manufacturer's instructions. For richer color, apply several layers of the stain, allowing it to dry with each layer applied. Apply a layer of non-stick concrete sealant to the stain 24 hours after the stain was placed using a low nap roller. Allow the sealant to dry before polishing the stained patio.
Polish the surface of the patio to a shine by changing to diamond resin based pads. Begin with a 50-grit pad and run over the surface of the patio to create a dull shine. Switch to successively finer grit resin pads moving through with each pass over the surface of the patio to create a brighter shine.
Finish the polishing process by spreading a layer of polishing compound onto the surface before the final run with a 3,000-grit pad to create a highly polished patio surface. Add a layer of epoxy coating with a paint roller to protect the polished patio surface and extend the shine.