Use a degreasing cleanser to remove any oil or grease from the concrete. Oil and grease keep paint from adhering to concrete and can result in the paint chipping and peeling later.
Rinse the concrete thoroughly and allow it to dry completely.
Repair smaller cracks or holes with concrete epoxy and a putty knife. If cracks are very small, you may want to leave them to contribute to the weathered look. If the concrete has any large holes or cracks, repair these with a concrete patch before painting.
Use an acrylic concrete stain to paint the concrete. Pour the stain into a paint tray and use a paint roller with an extended handle to roll the stain evenly onto the floor. Acrylic concrete stain is available in a wide variety of colors, so you can stay close to the concrete's natural color or choose a more daring shade. Allow the stain to dry according to package directions.
Mix 2 parts acrylic glaze with 1 part of your original acrylic stain in a small bucket. Mix 2 parts of acrylic glaze with 1 part of a different shade of acrylic stain in another bucket. For best results, choose colors that coordinate. If you're staying true to the gray color of concrete, choose a darker shade of gray or use a brownish shade. These two mixtures will help give the faux finish more depth.
Apply each shade of glaze with a separate paintbrush. Layer the two colors to provide a depth to the shades that will mimic weathered conditions. Allow the glaze to dry according to directions on the package.