You can take a bus from Pathein or Yangon. The roads are better now , so for the about 260km from Yangon it will take about 5 hours, depending what bus you take. There are morning buses (i.e. 6:30am and 7:30am depending on demand, 9000 kyat) and night buses that depart from the western Yangon bus terminal (Hlaing Thar Yar Bus Terminal) which is 45 minutes by car taxi from the city centre. There is a bus service (4000 kyat) departing Pathein for Ngwe Saung at 2:00pm again depending on demand, if you miss that hire a moto taxi or jump in a jumbo for 5000 kyat or less (bargain hard!).
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.
As at 16 July 2013 there is no longer a requirement to remit a copy of your visa and passport prior at a military check point on the way to Ngwe Saung.
You may rent a bicycle, scooter or take up the services of nearby bicycle, moto and car taxis.
Moto taxi trips within the township cost 500 kyat and 1000 kyat to the resorts to the North and South (up to a 5 minute trip).
Motorbikes (Honda Wave clones from China) can be hired for the day from most hotel receptionists for 10,000 kyat or less, there is no insurance and it is in most cases the hotel staff's own bike so take care of it and be sure to get it checked out prior to hiring if there are any known issues with the bike. The closest international standard hospital is Yangon's General Hospital which is at least 5 hours away.
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.
Local 'tea shops' have popped up within the township and to the North which offer cheap Myanmar brewed lager and stout beers and are busy throughout the day with local customers.
A bottle of Mandalay Rum can be purchased within the township for 1,500 kyat, 4 cans of coke will cost you 2,000 kyat (bargain for bulk purchases).
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.