Almost everyone arrives by ferry from Singapore. Several operators (Berlian, Penguin, Sindo, Majestic) run hourly crossings from HarbourFront Centre to either Sekupang (50 minutes) or Batam Centre (around 70 minutes); a return ticket costs roughly S$30 from Singapore or about S$20 from Batam. There are also ferries to and from Tanjung Pinang on Bintan and from Johor in Malaysia.
By air, Hang Nadim International Airport on the eastern side of the island has frequent domestic flights to Jakarta and other Indonesian cities, with several daily services on Lion Air, Citilink, Batik Air and Garuda.
Visas: most Western passport holders get a free 30-day visa on arrival, but check current rules before you travel — they change. Batam runs one hour behind Singapore, so factor that into ferry timetables.