Most stores open from 9 AM to noon or 1 PM and from 2 PM to 6:30 PM, although some remain open between noon and 2 PM. Shops are open from Monday to Saturday. Hotel stores have varying open hours so check at your hotel for these.
Above all, it appears that Arubans are very aware that their economy is completely dependent on tourism - so Arubans are polite to tourists, and even street vendors don't generally seek to rip off their customers though as in all traveling, don't let advice like this lull you into a sense of complacency. This may be helped by the fact that Aruba is a relatively expensive place to visit, so it tends to attract the reasonably well-off.
American dollars are accepted virtually everywhere at a decent exchange rate. If you have U.S. dollars, there is no need to change money into the local currency, the Aruban florin. The current exchange rate as of April 2008 given in shops is about 1.79 florins to the dollar. Because the island is a Dutch dependency, Dutch currency is easy to spend, and small change for purchases in dollars may be in florins. The island is actually not duty-free, but merchants respond well to competition on other islands, and duty free goods are offered by a few shops at the airport as visitors depart.
Oranjestad's waterfront has many vendors/stalls selling souvenirs. Ironically, many of these souvenirs are imported from the United States with island scenes/slogans, only to be purchased by Americans and brought back to America.
In Oranjestad, the Renaissance Mall contains various American and European major apparel brands i.e. Tommy Hilfiger, Polo Ralph Lauren, Gucci at essentially the same prices as in the United States. The mall and the rest of the downtown area also hold numerous other types of stores catering to visitors, to include jewelers, souvenir shops, clothers, and two modest grocers.
You'll find strip malls and grocers at modest not easily walked distances west of downtown and elsewhere. They offer most everything a visitor or resident might need for short stays or living there. Groceries and other supplies are all imported, so prices tend to be high. You can catch the bus from the hotel areas to the Grocery shops which are about 10 mins from Eagle beach but before you get to Oranjestad, cost's $3 return just ask the driver.
With numerous cruise ships visiting, downtown stores offer buys in jewelry, etc., typical of that in other Caribbean cruise ports, some at "duty free" prices. For cheese lovers, mild Dutch Gouda, in boxes or wheels, is a popular buy in super markets, though not the great bargain it used to be. Do ensure the integrity of the package seal from the maker to avoid spoilage and difficulty at customs inspection.
If you've flown to the island and are returning home, the airport duty-free store offers some items at slightly better prices than downtown, e.g., a decent selection of rums.