An agate is usually a portion of volcanic rock with brilliantly-coloured bands, defining the different siliceous layers deposited over many thousands of years. Agates, once polished, make beautiful pieces of art and are frequently used in jewellery and other applications. However, they are very hard stones, much harder than most stones recommended for polishing by hand. They can be polished by hand, but the process will take much longer than for stones that are less hard.
Clean the stone well with water to remove any dirt or debris.
Dip the agate in water before sanding.
Rub the surface of the stone with a harsh grain of sandpaper, such as 50 grit, if it has never before been polished.
Keep dipping the stone in water to make sure it stays wet while you're sanding it. Once the stone is the shape you want, move up to 160-grit sandpaper.
Rub over the scratches made with the coarser sandpaper to remove them and reduce their size.
Continue dipping the stone in water to keep it wet as you sand.
Use finer and finer grits of sandpaper in stages, up until 1500 grit.
Mix up powder polish and polish the agate with the polish and a piece of denim cloth until it achieves the shine you're looking for. Powder polish can be found in most hardware stores.