Branched coverings of the Riemann sphere

Question

Can someone give me an example of a non-trivial branched covering of the Riemann sphere?

Is there some way to enumerate all such coverings?

Is there any easy answer to the same questions about the torus?

Answer 1

Perhaps the simpler example is the map $z \to z^2$ from $\mathbb{C} \to \mathbb{C}$ and then extended in the obvious way to a map from the Riemann sphere onto itself. Could you see where it has the ramification points ?