  We give an explicit description of fundamental domains associated to the
$p$-adic uniformisation of families of Shimura curves of discriminant $Dp$ and
level $N\geq 1$, for which the one-sided ideal class number $h(D,N)$ is $1$.
The obtained results generalise those in \cite[Ch. IX]{Gerritzen_vanderPut1980}
for Shimura curves of discriminant $2p$ and level $N=1$. The method we present
here enables us to find Mumford curves covering Shimura curves, together with a
free system of generators for the associated Schottky groups, $p$-adic good
fundamental domains and their stable reduction-graphs. This is based on a
detailed study of the modular arithmetic of an Eichler order of level $N$
inside the definite quaternion algebra of discriminant $D$, for which we
generalise classical results of Hurwitz \cite{Hurwitz1896}. As an application,
we prove general formulas for the reduction-graphs with lengths at $p$ of the
considered families of Shimura curves.
