- If you are flexible about your travel dates, start with SkyScanner. It has the best interface I've seen that lets you pick between dates and prices.
- Once you've used that to narrow it down, you'll probably find it's offering you flights by certain carriers through resellers like Expedia or the like. Doublecheck SkyScanner's price with the reseller. Then go the carrier's own website and see if it's the same price there.
- Optional: either call or go and visit some actual travel agents and try and beat that price. Or try some other websites, like NetFlights, which just so happens to use the software I work on every day for flight prices.
- If all these prices are about the same, book on the carrier's own website. You'll get the least chance of anything going wrong that way, and the best chance of things like online check-in not screwing up. If the prices are different, or the best fares are ones that combine different carriers, then book wherever the price is least.
And don't forget your ESTA, as Pete has said, and make really,
really sure that your APIS data (name, address, passport) that you enter on the booking is absolutely correct.