  In this paper we give an algorithm that calculates the skeleton of a tame
covering of curves over a complete discretely valued field. The algorithm
relies on the {{tame simultaneous semistable reduction theorem}}, for which we
give a short proof. To use this theorem in practice, we show that we can find
extensions of chains of prime ideals in normalizations using compatible power
series. This allows us to reconstruct the skeleton of the covering. In studying
the connections between power series and extensions of prime ideals, we obtain
generalizations of classical theorems from number theory such as the
Kummer-Dedekind theorem and Dedekind's theorem for cycles in Galois groups.
