Decide what you are looking for ahead of time. Not only does this keep you from going bargain crazy, but it's pretty fun hunting down the best price for a bottle of your favorite top shelf liquor and helps kill layover time at the airport.
Be forewarned that cruise ships require you to check your duty free liquor upon re-entering the ship, so even though, in theory, you could save big bucks by BYOB'ing it rather than paying 12 bucks for a margarita, you won't be seeing that liquor until you disembark at the end of your trip.
Do your research online. It may seem like you are at the mercy of being in a foreign country and not knowing whether you're actually getting a good deal, but if you have access to the internet, visit The Duty Free Price Guide to compare duty free product prices around the world. That way, you can rest assured that the $75 bottle of Chanel No. 5 in Dublin actually is a good deal compared to the $105 you'd pay at Brisbane Airport.
Educate yourself on any restrictions regarding the amount of duty free products you are allowed to take out or bring back into the countries you are visiting. Each country has different regulations.
Find out where the duty free shops are and if they specialize in anything. While your only chance to score duty free prices may be in airports, some destinations are incredibly bargain friendly. For instance, the Vatican is duty free and cruise ships offer the duty free basics as do all the cruise ports, but also look out for Hello Kitty merchandise in Tokyo, ethnic wedding dresses and canned spices in Mexico and maple syrup in Montreal.