Grab your passport. Starting at Tanah Merah MRT station, take bus 35 to the Tanah Merah Ferry Terminal (they run every 10 minutes). Buy a ticket to Nongsapura ferry terminal. Departures are at 08.00, 08:55, 10:00, 11:00, 12.00, 14.20, 16.20, 18.30, 20.30. Get there at least 30 minutes before to buy your ticket and pass through immigration.
On arrival at Nongsapura, you can then choose to either:
Total travel time from Tanah Merah MRT to Nongsa Point Marina, including passing through immigration: ~ 2 hours.
Get yourself to the airport. Take a flight from Jakarta to Batam (flight time 1½ hours). Then get a taxi to Nongsa Point Marina (~ 20 minutes).
Total travel time: ~ 2 hours.