Constructs are artificially created objects that have been imbued with a magical semblance of life. Most commonly they are made in the shape of humans and in such cases are generally called golems. That said, constructs can be of any form. In the glory days of the city, creating a living construct out of ordinary household furniture was quite popular.
Golems and other constructs can theoretically be created out of any material. Wood, metal, and clay are the most common as they are the easiest to work with, but constructs made of stone, bone, plants, and even paper are all possible. For game purposes, the actual material used is irrelevant.