What's The Best Way To Find IT Jobs In Singapore?

Wow! Singapore's a great place!
As always, when trying to relocate to a new country and find a new home, employment, schooling, etc.,  probably your best bet is to contact both the Chamber of commerce in your state and in the country you're relocating to.
These sources have all the relevant information at their fingertips. (A veritable one stop shop, if you will).
They will help to remove a whole lot of the guess work a newcomer will have to deal with , and can point you in the right direction.
Just tell them both what your plans/needs are, and they can give you the relevant information. (They may even set you up with a liaison in the country from their office).
The American embassy over there, as well as Singapore's embassy in your state, will also be a great source of information.
Hope that helps.
I wish you good luck, and God-speed.