  We provide an alternative, constructive proof that the collection
$\mathcal{M}$ of isometry classes of compact metric spaces endowed with the
Gromov-Hausdorff distance is a geodesic space. The core of our proof is a
construction of explicit geodesics on $\mathcal{M}$. We also provide several
interesting examples of geodesics on $\mathcal{M}$, including a geodesic
between $\mathbb{S}^0$ and $\mathbb{S}^n$ for any $n\geq 1$.
