Can somone provide me (articles/literature) with examples of Chow rings of surfaces?

(e.g. here: http://www.math.uni-bonn.de/people/huybrech/K3Global.pdf Chapter 9)

What I want is a list of (smooth projective surface $X/\mathbf{F}_q$, $CH^*(X)=CH^0(X)⊕CH^1(X)⊕CH^2(X)$, the product structure on this, $\mathrm{deg}: CH^2(X) \to \mathbf{Z}$ and the ample cone).