Here are the ways:
1) Demand Draft. Cheapest of all options but also slowest of all options. Commission is only 0.125% or S$10 min for most banks. It takes about 1 month+ to clear. One advantage is that you do not need to have an existing US bank account, you can bring it with you and deposit there.
2) Telegraphic Transfer. Not as cheap as Demand Draft but faster. Commission is 0.125% or S$10 min from most banks, plus there is a fixed S$20 cable charge (so total S$30 commission). It takes about 1 week to clear. You must have a US bank account to receive money by TT.
3) Traveler Cheque. Good only if you are transferring less than S$1000 over, as the commission rate is high at 1%. However, it is cleared very fast, usually within a week unlike Demand Draft. You also do not need to have an existing US bank account to purchase this.
4) Citibank Global Transfer. If you plan to create a Citibank US account over there then you can set up a Citibank SG account and use their "Global Transfer" service. Commission is cheap at a flat rate of $10, but Citibank FX rate is higher than other banks (compare to DBS which IMO has the lowest FX rate). Also note that the maximum you can transfer is S$3000 - I think the limit is per week pls check. One advantage of Citi Global Transfer is that it is instantaneous. You must have a Citibank account at both countries for it to work, and the minimum sum to maintain Citibank accounts is not cheap.
5) PayPal. Set up a paypal account and link it to your SG bank account and your US bank account. Then transfer from SG Bank -> Paypal Account -> US Bank. Process takes about 1-2 weeks, and PayPal has the most ridiculous FX rate.
6) HSBC Premier Account. If you have a HSBC Premier Account you can ask HSBC to create a US HSBC account for you in Singapore. I think they have free transfers as well between HSBC accounts. However, to be a Premier customer I think you need to park loads of money with them. Probably not accessible for most people.
7) US-Based Broker (e.g. optionsXpress SG). Open a broker that is US-based, fund the brokerage account and leave the money as cash. When you get to the US, open a bank account and link it to your brokerage. Most US brokers support ACH transfer (it's like GIRO) and the money will be in your bank within 2-3 business days.
8) Wells Fargo IPB. It's not a transfer method, but you can open a Wells Fargo US bank account from Singapore by going through the IPB website. This way, you can get the check book, debit card and US bank account all established and sent to you in Singapore before you go. You can then also initiate a TT in Singapore before leaving.
Sample FX rates when I was transferring money a few days back:
DBS: 1 USD = 1.40 SGD
Citibank: 1 USD = 1.41 SGD
Paypal: 1 USD = 1.43 SGD!!!
Personally, if I do not have a US bank account, I'll probably bring cash and Demand Draft. However, if you need a lot of money within a month, then perhaps you should consider finding a bank that allows you to do Telegraphic Transfer through internet banking.