The Greeks made most of their sculptures from marble, a rock substance that is widely available in Greece. While there are a variety of types of marble, the Greeks preferred marble that was off-white, since it offered better contrast when viewed, enabling viewers to better see the curves worked out by the artist. Greek artists also had the option of working with a finer grain marble, which yielded better detail but tarnished more easily, or a coarse grain marble, which was less conducive to detail but offered a shinier finish in the long-run.
For the most part, the ancient Greeks relied on two tools for working on their sculptures --- a hammer and chisel. The chisel is a simple length of metal, usually in the form of a bar, shaped somewhat like a nail, but with a flatter edge. The Greeks would place the flat, sharp, edge of the chisel on the marble, and then used a hammer to strike the chisel in order to form the marble into their artistic vision.
Since the marble that the ancient Greeks were using was, more or less, coarse, it needed to be smoothed out in order to accentuate the curves of the piece. In order to do this, sculptors used an emery stone, similar to a piece of sandpaper, to develop the curves in the sculptures and to accentuate certain areas of the piece.
When we think of ancient Greek sculpture we think of the off-white statues that we are used to seeing in museums. The ancient Greeks, however, usually painted their sculptures --- especially their statues --- with several colors of paint including blue, red, brown, and even orange. Specialized painters were employed to add the color to a sculptor's work once it was finished. Over the years, the paint on these sculptures has worn off, even though a sealant was used to help preserve the paint job.