  Let $k$ be a perfect field and let $C_0:f=0$ be a smooth curve in the torus
$\mathbb{G}_{m,k}^2$. Let $\mathbb{T}_\Delta$ be the toric variety associated
to the Newton polygon of $f$. Extending the toric resolution of $C_0$ on
$\mathbb{T}_\Delta$, we construct an explicit model over $k$ of the smooth
completion of $C_0$. Such a model exists for any smooth projective curve and
can be described via a combinatorial algorithm using an iterative construction
of Newton polygons.
