There are only two ways to get into Batam depending on where it comes from.
By plane or by ferry.
There is only one airport here, Hang Nadim. This is an international airport.
And several seaports, domestic and international, such as Sekupang, Harbor Front, Batam Center, Nongsa Pura, Marina City, Batu Ampar and Punggur.
From port (sea / air) to your destination (hotel / resort), you can use taxi or public transportation (called TransBatam).
Arrival
The option after you came out from the airport are
Using taxi airport
Using Airport bus (about 25k IDR or 1.8 USD)
Route to Jodoh
Route to Batu Aji
Walk out the airport area, on foot, to the intersection (about 500 m) and catch public transportation such as TransBatam (coridor 6) to Batam Center or Nongsa (4k IDR/0.3USD), or small vehicle (same destination but different route).
Tips, please be aware / be careful if you plan to use taxi on-line (grab, uber, go-car)
Departure
You can use all above option and taxi-online.
Thanks for the tip, @nusdjo ! I’ve been to Batam twice and both times I arrived via ferry from Harbourfront.
What I’m really interested in is what visitors can do at Batam! 
Thanks for the comment Jes,
I’ll post related with transportation from HarbourFront. And related with your interest, may I know the scope? For vacation or business ?
Leisure! It’d typically be a weekend or maximum 3-days trip as we couldn’t seem to find anything to do at Batam! Hoping to discover more of Batam, maybe you can share some @nusdjo !
best wishes for you:tulip:
@JeslynL wrote:
Leisure! It’d typically be a weekend or maximum 3-days trip as we couldn’t seem to find anything to do at Batam! Hoping to discover more of Batam, maybe you can share some @nusdjo !
@JeslynL contact me when you plan to go to batam next, I’ll arrange a private tour with you. I am a local guides here and have mapped most of Batam
This is becoming a small guide book for Batam, can’t wait to see more! Thanks all for sharing!