It's simple to reach Swanage Beach, in Swanage, by train. Simply hop on a train to Wareham station and then it's just accessible by train on Summer Saturdays. SWR trains run to Wareham, then on to Corfe Castle. You can pick up a connecting steam train on the Swanage Railway which takes you right to the seaside! The map here shows the simplified route from Wareham station: there are also frequent buses from here too..
Swanage Beach in Swanage is an absolute classic seaside destination.