Look for items that you've priced in other places. Otherwise, you're at the mercy of the merchant.
Buy at the end of the trip.
Bulky purchases can slow you down, and mailing the items home can take a bite out of the tax savings. Another reason for this is comparison shopping. Is the Delft china at Amsterdam's Schiphol Airport really a better buy than what is sold in the city? You won't know until you've been both places.
Know the rules before you go.
The European Union has done away with many of the tax free laws that once existed when the nations of that continent had a more individual approach to commerce.
But there are in-airport bargains there (at least that's how they're advertised) because it's still possible to bypass Value Added Taxes (VAT). This is a sort of local sales tax you pay throughout Europe, but it is completely refundable if you are not an EU citizen.
Many people either don't know VAT is refundable, don't know how to obtain a refund, or just don't want to be bothered with it.
The beauty of these shops is that the tax is not charged. Again, you must be knowledgable enough to know if the VAT-free price is lower than what's available at home.
Be aware that duty-free at point of purchase does not necessarily mean duty-free when you get home! There are limits your home country imposes on citizen purchases abroad. There is a total that is free of duty (for United States citizens, it's usually $400-800), but spending sums beyond that amount could result in a duty charge.
There are also rules specific to individual locales. For example, in the Virgin Islands you may purchase up to five "fifths" of alcoholic beverage and bring it back to the U.S. duty free. Other ports usually only allow one "fifth."
Are you beginning to see why it pays to know the rules?
Visit appropriate Web sites before departure.
A cruise line that lists the Virgin Islands among its ports-of-call will probably have information about the duty-free alcohol on its Web site. The airline that offers specific bargains while in flight is going to list those somewhere, too.
Your destination's tourism bureau is going to tell you what's hot in their shops and bazaars, and the duty-free rules that apply.
Don't let shopping dominate your trip.
This might be the best tip of all. Some travelers become so obsessed with finding the perfect bargain that they miss out on a lot of other enjoyable experiences. When that happens, you waste money--because you waste precious time, too.