Before you're ready to paint any concrete surface to look like stone, you have to select what colors the stone will be. Note that no stone is one uniform color. There's a basic background color, then small mottles or flecks in other colors. Choose your paint or stain colors accordingly, with one primary background color and at least one or two complimentary colors for the flecks and specks in the stone. Because concrete is so porous, you may want to use special concrete paint or stain products to achieve the best results.
Clear any furniture or other large materials off the concrete, then sweep it clean of debris and, if necessary, scrape off anything. Let any damp sections of the concrete air-dry until they're completely dry.
Tape off any areas that aren't meant to be painted, using either masking tape or painter's tape.
Paint the concrete with two coats of the primary stone color you've chosen. Use either a roller or a brush to apply the paint, depending on the size of the area to be painted. Let the paint dry after each coat.
Wad a plastic grocery bag up into a ball and dip this into one of the complimentary paint colors you've chosen. Daub the paint across your concrete surface, patting it into place with the bag instead of wiping or brushing.
Repeat the dip-and-daub process with other porous materials, such as wadded-up tissue paper, sea sponges or mesh shower balls, to add variety to the textured pattern you are creating. You can also stick with the plastic bag if you like the patterns if it creates. This is art, so there's no one right way. You may want to experiment on a board or less visible place to find out which gives the most pleasing texture for you.
Brush a feather duster across the wet paint surface to help blend the colors together.
Wait until the paint you've applied has completely dried, then finish with a coat of clear paint, stain or varnish to protect the painted surface.