what do the demand and supply curves for a free good look like?

Answer 1

Demand will look the same, sloping downward. The amount demanded at $0 will be the maximum demand for the good.
Supply will be a bit different. It will slope horizontally along the x axis for a while, but would eventually move upward. It could also be argued that the supply curve would slope down into the negative price range. However, the type of good you are probably thinking of would not exhibit this, since most entities would not pay to have the product taken away.