A sieve does its work through simple mechanical selection: a mesh, woven from cloth, wire, or another material, is stretched across a rigid frame so that it presents a surface full of tiny, evenly sized openings. A ground or powdered material is placed on top of the mesh and the sieve is shaken, tapped, or worked, and as the powder moves across the mesh's surface, any particle small enough to fit through one of its openings falls through to a collecting vessel below, while any particle too large to pass is held back on top.
Continued shaking works the powder across the whole surface of the mesh rather than letting it sit in one spot, giving even the finest particles a chance to find and pass through an opening while steadily separating out anything still too coarse. The size of the mesh openings set exactly how fine the final product would be, so an alchemist or pharmacist kept sieves of several different mesh grades on hand, choosing a coarser one for a quick rough separation or a tighter one when an operation, dissolving or subliming a mineral especially, needed a powder ground and graded as fine and even as the workshop could manage. Material caught on top of the mesh could simply be returned to the mortar for further grinding and sieved again until it passed.