The gantries cover:
a) the down-town part of the island (CBD - Central Business District), and,
b) the Expressways.

Different gantries are active at different times:
a) CBD - generally daylight hours on weekdays, and
b) Expressways - from early morning to 9:30am weekdays.

So, with some clever oversleeping (for the Expressway charges), and some nifty route-planning for the rest of the day (to avoid the CBD network), you can opt not to install one and keep hold of your cash.

Suffice it to say, I took this option.

If you must be expressway-dwelling before 9:30am, or must cruise downtown during weekday daylight hours, then you have the option of outright purchase or renting and IU. The LTA have information on this.

The official LTA guide to ERP (Electronic Road Pricing).

It shows all locations of the gantries, and their times of operation.

It is freely available from the LTA offices at Sin Ming Drive.

Autopass Card
This is used to pay the Vehicle Entry Permit (VEP) fees, or road tax.

Noting that I brought my vehicle in at the port, and not at a land crossing, this is the way it worked for me:

The AAS (Automobile Association of Singapore) issued me with an ICP (International Circulation Permit) for which they charged me OSAM (Only a Small Amount of Money), but made me buy insurance for a HAM (Huge Amount of Money). With this, I went to the LTA (Land Transport Authority) where FGE (Friendly Government Employees) told me to return on my LDS (Last Day in Singapore). Then I could collect an Autopass card with one day's VEP (Vehicle Entry Permit) which would allow me to CIM (Cross Into Malaysia).

Now, according to all literature, I was supposed to pay VEP for every day in Singapore. Don't ask me why three people in the LTA told me only to pay on the day of departure. In the complaints queue, I was nowhere to be seen.

I drove all around Singapore for a week, avoiding active gantries, and returned to the LTA at Sin Ming Drive on the day of depature. Purchased an Autopass card for S$40, S$30 of which was for one day's VEP (deducted from the card there and then), and another few dollars for the Causeway toll.