Italy's Treneitalia rail network serves Praia a Mare with trains running approximately every two hours. The station can be easily missed, as it is a hub for two other nearby villages as well: look for Praja, not Praia a Mare, when preparing to alight the train.
It is possible to rent small watercraft on the beaches adjacent to the promenade 1-2km south of the village center. Avoid berthing boats in the area just south of Dino island, especially in the summer--that area is reserved for swimmers.
To visit Dino island, the most complete experience would be to join one of the tours departing from Capodarena, either on smaller or larger boats, taking you around the island as well as to the Arcomagno bay, further south.