We address the efficient finite element solution of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers (PMLs). The PML is a popular non-reflecting technique, which combines accuracy, computational efficiency and geometric flexibility. Unfortunately, the effective implementation of the PML for generally-shaped convex domains is tricky because of the geometric parameters that are required to define the PML medium. In this work, a comprehensive implementation strategy is proposed. This approach, which we called the automatically matched layer (AML) implementation, is versatile and fully automatic for the end-user. With the AML approach, the mesh of the layer is extruded, the required geometric parameters are automatically obtained during the extrusion step, and the effective implementation relies on a simple modification of the Jacobian matrix in the element-wise integrals. The AML implementation is validated and compared to other implementation strategies using numerical benchmarks in two and three dimensions, considering computational domains with regular and non-regular boundaries. A three-dimensional application with a generally-shaped domain generated using a convex hull is proposed to illustrate the interest of the AML approach for realistic industrial cases.