The craft economy of Xi'an grew out of two things: the terracotta army, which made reproduction a local industry, and the scholarly tradition of the city, which supported brush, ink and paper making for centuries. Most of what you see near the sites is factory work. Some of it is not, and the difference is visible if you know what to look at.
Terracotta replicas
Replicas range from keychain-sized to near life-size. The mass-produced ones are cast in molds, uniform in color and cheap. Better workshops hand-finish the cast, apply a clay slip to reproduce the original surface, and break the uniformity of the face so no two are identical. Large hand-finished pieces are heavy; ask about shipping before you commit.
Shaanxi folk crafts
Paper cutting here is a genuine folk tradition, with designs for doors, windows and weddings in the local idiom. Shadow puppets, made from cured donkey hide and painted in translucent colors, are a real regional craft and are sold as both framed pieces and working puppets. Huaxian peasant paintings, from the county west of the city, are bold, dense compositions in strong primary colors and are among the most distinctive things made in Shaanxi.
Calligraphy
Near the Stele Forest there is a cluster of shops selling brushes, ink sticks, inkstones and paper. A brush with a wolf-hair or mixed tip is the standard working tool; goat hair is softer and better for larger characters. Inkstones from the region are sold as both working tools and display pieces, and prices vary enormously by carving.
Practical notes
Bargaining is expected in the markets around the Muslim Quarter and at the terracotta site, but not in the established brush shops. Confirm that wood, hide and clay items meet your country's customs rules before buying. Keep receipts for anything over a modest value.
