You should decide on your payment gateway first. Look at their fee structure.
I think the one closest tied to local banks is the
d2pay by DBS/POSB.
I have seen some local businesses using
WorldPayor
PayPal.
There are many others out there. Just google for "Singapore payment gateway".
Anyway, once you subscribe to their service, they'll provide you with the technical details how to integrate their payment system into your e-commerce platform.
Usually they have some JavaScript which you need to include in your web page, and possibly your form fields/parameters need to be named and values encoded in certain way when passing transaction data to their server.