Let $\gamma$ be a closed curve, and $a\in \mathbb{C}-im(\gamma )$, and denote $n_{\gamma }(a)$ its 1. Definition 2.9.1 - winding number

If $a$ crosses $\gamma$ from the "right side" to the "left side", the winding number $n_{\gamma }(a)$ increases by $1$

This provides an algorithm to find the winding number given that the winding number of a point in the unbounded component is $0$.