Fabric, surface, and how it was formed.
Look first at the fabric in a fresh break: colour, hardness, and inclusions (sand, grog, shell) all help place it. The break tells you more than the decorated surface ever will.
Wheel-thrown pots show fine spiral “throwing rings” inside; hand-built and molded wares do not. Glaze, slip, and paint sit on the surface and can be later than the body.
Rims are the most diagnostic sherds — a rim profile can often be matched to a published form series and give a date range on its own. Note sooting, limescale, and wear inside the base too: they record how the pot was actually used.
Black-figure and red-figure Greek wares, glazed medieval jugs, and unglazed earthenwares each have distinct fabrics and finishes — compare against published types, and record fabric, form, and surface treatment as three separate observations.
Identifying terracotta figurines
Identifying amphorae and transport pottery