There is a road north to Dawei, but foreigners are not permitted to use it.
By plane
Myanma Airways has daily flights, and Air Bagan has 3 flights per week, from Yangon. Myanma Airways flights typically once a week to Mawlamyine and Kawthoung may also be available - check locally at the local Myanma Airways office.
Flights may be canceled with little or no advance notice, due to lack of bookings, the weather, or any number of other unpredictable circumstances.
By ship
Fast ferries run daily to/from Kawthoung ~6 hours, US$25 for foreigners and most days to/from Dawei to the north ~4 hours, US$20 for foreigners.
Five Star Line passenger ships may call here approximately fortnightly en route from Kawthoung to Yangon and/or vice-versa. Five Star Line have an office opposite the main piers. Foreigners must pay very high prices ~US$100+ but the first-class 2-berth cabins are quite comfortable.