You can take a bus from Pathein or Yangon. The roads are better now , so for the about 260 km from Yangon it will take about 5 hours, depending what bus you take. There are morning buses (i.e. 6:00 AM) and night buses.
You can also go by boat from Yangon to Pathein.
Hiring a car is only worth it if you have missed the morning bus and do not want to ride by night. The difference in time is not big.
Note: Make at least 1 paper copy of your visa and passport as you will need to remit one at a military check point on the way to Ngwe Saung.
You may rent a bicycle or take the bicycle taxis.
The endless and quiet white sand beach. There is also an 'elephant camp' in between Ngwe Saung and Pathein.
Several comments conclude that snorkeling in Lover's Island is rather a disappointing experience.
Go to the beach, see the local village. There is not much to do in Ngwe Saung, that's the idea. Just relax and enjoy the quiet time.
Painted umbrellas made in town or in Pathein.
There is no disco, however the very modern and stylish Bay of Bengal hotel has sometimes disco like events.
By bus: Yangon is 5 hours away. The road is reliable and the bus is comfortable. Buses depart in the morning (8:00 AM). Ticket can be purchased at a traval agency opposite the Jasmine Restaurant in town. As of May 2013, a one-way ticket to Yangon costs 9,000 kyats. Note that the station at Yangon is about 45mn to 1h drive by taxi, which is 8,000 kyats.