The trick is signing up for credit cards with good bonuses. The best on is the Starwood Preferred Guest (SPG) American Express card. Not hard to get approved, and if you spend $3000 in the first 3 months you get 50,000 points. These can be converted to miles on any major US airline, plus you get a 10% bonus. So that's a total of 55,000 miles. Can pay for a roundtrip to Europe or anywhere in South America (as long as its not peak time). Miles are generally worth about $0.01 per mile so this ends up being worth $550. Not bad at all!
The other important thing is picking a time to fly when there is less demand for tickets. The cheapest days to fly are Tuesdays and Wednesdays.