I do have a DBS Vickers account, but I'm not sure how I can buy US stocks. Anyone can guide me please, and let me know if this is a cost-efficient way?
You should just be able to select which exchange you want to trade on - or search for the appropriate stock. (Try searching for SPY - the S&P 500 index fund - and look for an exchange called NYSE or Arca.)
It's most definitely not a cost-efficient way to do it, though. DBS's FX spreads are on the wide side (and they charge the spread on the way in and the way out); their brokerage fees are extortionately high; and they charge needless custodian fees and dividend fees. Don't ever buy US stocks through Vickers.
related question
how about SGD=>USD currency conversion? how to get cheap conversion?
Depends. Do you want the cash for holidays; do you want to use it to buy something over there; or do you want to use it to trade?
If you want it for holidays, just go to Change Alley. If you want to buy something over in the States, go to your bank and demand a discount on the posted spread. If you want to use it to trade, open up an Interactive Brokers account and take advantage of their tight FX spreads.