The island is arguably the biggest shopping mecca in the Caribbean. Goods are imported to the island duty and excise free, and visitors do not directly pay any duty or tax on purchases (merchants do pay a Gross Receipts Tax of 5%.) Buyers may face Customs duty as they return home if they exceed their Customs exemption.
U.S. currency is used/accepted universally. ATMs can be found in numerous locations. As anywhere, major purchases should be made by credit card. (Credit cards issued by U.S. banks do not induce foreign-exchange fees, others may.) Most store-front establishments, resorts, and restaurants accept credit cards and traveler checks. Few places accept personal checks. Sellers in open-air bazaars may not accept credit or debit cards.
You can shop many dozens of stores downtown (in Charlotte Amalie), and others in a few malls dotting the island, and near cruise ship docks, e.g.:

• Havensight. Has many of the same shops as downtown, but in smaller versions.
• Yacht Haven Grande next to Havensight offers restaurants and premium branded stores.
• Crown Bay has a modest number of stores similar to Havensight (most closed when no ship is docked there).
• You'll see Pueblo Supermarkets (modest by mainland standards) near Havensight and Crown Bay.

You'll find numerous tent kiosks at Vendor's Plaza at the near southeast side of downtown...across the highway from the waterfront. There you'll see many colorful offerings in shirts, caftans, rainwear, etc., often marked with USVI scenes or logos, most manufactured elsewhere. Other stores in resorts, strip malls, etc., tend to serve locals and land vacationers; many of them open on Sundays, e.g., K-Mart (one walkable from Havensight) & a larger store in Tutu Park.
In many stores, gems, jewelry, watches, liquor, cosmetics, perfumes, linens and (sometimes) cameras, optics, electronics, and fine crystal and china can be good buys but know the costs for the same/similar items back home. (Some cameras, optics, and electronics may be obtained at home from aggressive discounters (e.g., on the Internet) for equivalent or lower prices. But those savings can disappear if those sellers charge sales tax, shipping costs, or extra for US-importer warranties.) Price advantages for U.S. citizens may be helped by generous duty exemptions. These advantages can make the economics of buying in the USVI slightly better for U.S. citizens than elsewhere (e.g., St Martin) where prices may be similar, sometimes better. However, unique, appealing or well-priced items seen elsewhere should not be avoided because of feared duty costs...often modest even if you exceed your exemption.
Bargaining is appropriate in open-air bazaars, and should be tried in stores but may be rebuffed in a few for some kinds of items. Here, ensure that items of interest that need any kind of (service) warranty have one in writing that is usable at home, e.g., for electronics, watches, cameras. You need to ask if any warranty is "grey-market", international or backed by the US-importer, and understand the consequences of what's offered. For valuable gems or jewelry, ensure the seller provides a written description and certified appraisal of each item's worth.
In exchange for very large fees paid by some merchants, "port shopping advisers" on cruise ships tout those merchants as more reliable than others, with passenger satisfaction "guaranteed, except for negligence or buyer's regret". Ultimately, you pay those fees. But most stores are quite reputable, ready to rectify any problem that's truly their responsibility. Touted or not, smaller retailers such as Artistic Jewelry and Mr. Tablecloth offer quality fully-equivalent to such large and famous stores as Cardow or A.H. Riise. And they may offer items seen nowhere else. The best approach...always thoroughly inspect any high-cost item and obtain a written/signed description or appraisal before accepting it.
Per "Get in" discussion above, when many cruise ships are in port, the open-air bazaar and stores can be crowded...sometimes very crowded. That can compromise bargaining success and how well you are helped even in the best stores with fine staffs. Shopping early or late can help avoid some of the crowds. Stores downtown (Charlotte Amalie) usually open at 09:30-10:00 and close around 5:00 PM. Half-day, morning ship's tours (the most popular) end about noon back at the ship, and ship itineraries often call for departures at 4-6 PM (with all-aboard as much as an hour earlier). You might time your shopping accordingly.
On Sunday, early can be essential. A few stores (mostly in downtown Charlotte Amalie) don't open, more open only if at least one cruise ship is in port, and many of those stores close by early-mid afternoon. Occasionally, local holidays/festivals make shopping downtown problematic due to street and store closures, e.g., for parades. Most carnivals/celebrations are in late April & early May.
Especially if you must fly to get home, you may wish to have stores ship out-sized or heavy items home for you (liquor, perfumes, and tobacco excluded). Costs for surface shipping can be modest, air a bit more but faster. (Your local Post Office, UPS or FEDEX store should be able to give you example costs. "Know Before You Go" noted below indicates the US Postal Service is more convenient for sending dutiable items.) Any method helps avoid the dangers of damage (or theft) by baggage handlers, greatly simplifies your return home, and allows you to refuse to accept (at/hear home) any shipment that appears damaged. There are requirements for documentation and customs labeling when shipping dutiable items. Retailers should help, and may even arrange everything. If significant customs duty will be involved, you may have to pay it at/near home as you receive the item(s). But ask the merchant if you can simply declare the item on your Customs form as you return home.
Several stores offer large and varied selections of quality and premium liquors (and other merchandise) at low prices rarely if ever seen in the U.S. For liquor, they include: A.H. Riise/Penha, Dynasty, Caribana and others downtown; many of the same names in Havensight, plus K-Mart, Pueblo Supermarket and Al Cohen's Warehouse near Havensight; A.H. Riise/Penha and Supreme Liquors at Crown Bay, with another Pueblo Supermarket nearby. Prices in most stores for popular brands are quite close except for scattered "specials". Prices for highly-premium brands may vary more. Most liquor comes in one-liter bottles (some larger), some US-produced and many European liquors come in .75 liter ("fifths"), and liqueurs may be in still other sizes. So take care when calculating or comparing cost per ounce or liter.
Some of those stores will box your purchases and deliver them to your ship the same day at no charge if you ask and purchase early enough. That way, you don't have to carry them with you the rest of the day. Others (e.g., K-Mart, Cohen's) usually have boxes available and may box bottles for you to carry. (Boxes/boxing and delivery may be the major difference among sellers.) If you have a choice, smaller boxes (e.g., 2-4 bottles each) are easier to pack and pad in luggage. Large purchases of liquor induce considerable logistics challenges, so plan ahead on what to buy and how to carry it back. If you are on a cruise:

• Any liquor you carry onboard will be collected, and returned to you on the last day of your cruise, in whatever container(s) you used to carry it. Use something for adequate padding, e.g., newspaper.
• Other bottles may be delivered to your ship, boxed for you by the merchant (sometimes with many other boxes wrapped on a pallet) and similarly and automatically collected by the ship's staff. They'll be brought to your cabin the last day of the cruise.

Customs and duties

The following discussion focuses on U.S. customs laws/procedures. Many of these basic processes are similar for travelers returning to other home countries.
You should always consult authoritative sources to obtain and understand the consequences of customs limits and duty costs before making major purchases, e.g., for U.S. Customs. Otherwise:

• You may face unexpected costs (duty levies) if you make purchases that exceed your duty allowances.
• Unscrupulous sellers may try to convince you that you enjoy far higher exemptions (and freedom from duty, inspection, and seizure of illegal items) that are untrue...just to make a sale.

Don't pay duty on valuables you already own and take on your trip.
Best-effort recap of U.S. duty exemptions: The following summarizes your duty exemptions/allowances as you return home having visited the U.S. Virgin Islands (actually any part of any U.S. protectorate) on any part of your trip:

• Liquor: Under a separate duty exemption, each adult U.S. citizen is allowed to return to the U.S. with four liters or five-fifths of liquor duty-free (up from one liter), provided at least half of the value was purchased in the USVI. If you purchase at least one liter of product made or bottled in the USVI (e.g., Cruzan rum), you can return with five liters/six fifths duty-free. (Otherwise, if you buy only outside the USVI, your exemption is one liter.) With different bottle sizes noted above, take care about numbers of bottles versus total liters purchased for your Customs declaration. Exemptions for wine and beer are different. Adult members of immediate families can "pool" liquor exemptions. If you moderately exceed your exemption, duty will be moderate.
  • Take care with large quantities, e.g., Florida treats more than 20 fifths or liters as a commercial importation, requiring in-advance an importer's license (not easily or quickly obtained, and involving an annual fee) and payment of state sales tax in addition to Federal duty and taxes. Without it, U.S. Customs is required to report such amounts, and to collect all duties/taxes from "licensed importers"...or to confiscate the items.
• Gems/Jewelry: U.S. Customs treats loose gemstones (even fully faceted) as "rocks" having no dutiable value. However, if mounted in jewelry, the full cost as finished jewelry must be declared. No reputable jeweler will separately sell you an unmounted stone and its mount to avoid duty; it would place them and you in violation of the law; if discovered by Customs, items may well be confiscated, with other actions possible.
• Tobacco: A separate quantity restriction applies to tobacco products. Overages may be confiscated.
• Blacklisted sources/items: Any goods made in Cuba (or other "blacklisted" countries), and items deemed contraband (e.g., certain animal or plant products) will be confiscated by Customs if found. Major amounts may generate a fine or result in arrest.
• Unique items: Original artworks created here/abroad and certain other custom-made items may also be treated as non-dutiable; you'll need a certificate of origin from the seller.

USGR/AGR You may find goods that were made in the U.S., e.g., some T-shirts, a few brands of jewelry. So ask the sellers. Such items are called "U.S./American Goods Returning" (USGR or AGR) and do not count against your duty exemptions. If so, ensure the seller provides a proper/formal indication on or with a receipt so that the cost(s) will not count against your duty allowance. Similar policy may apply for products made in and returning to other countries.
All purchases (including USGR/AGR) and gifts you've received (except what you've consumed or given away before returning) must be itemized on your customs declaration; USGR/AGR and other exempted item costs should not be included in the dutiable sum of your purchases. Have receipts, certificates, and merchandise for all listed purchases readily at hand as you pass through Customs. Be sure to list any food products by type.
As you return home (U.S. mainland or Puerto Rico)...

• While on your ship, you'll be instructed to fill out a Customs form.
• And go through Customs, have purchases, receipts, Forms 4457 and the Customs declaration form handy to show officials. They may opt not to charge duty for purchases in slight excess of any limit. They will often charge for each limit exceeded if you are paying duty for other purchases anyway.

Other customs enforcement (e.g., for Canada or EC countries) depends on country limits and customs diligence.

Returning home

(Emphasis U.S.; please expand):

If cruising, you'll probably go through customs processing at the port where your cruise ends. If you then return home by land (e.g., drive), you'll be weight/size limited only by your vehicle and your ability to carry everything off the ship...at least just before you claim luggage in the terminal that has been carried ashore for you.

Purchases may be too numerous or heavy to be hand-carried on flights even if permitted. Compare luggage fees you'll encounter with the cost-savings you may see at purchase. Fees may considerably outstrip savings. (Yes, these realities have greatly affected merchants' business worldwide.) If you have weight or size challenges, consider shipping what you are allowed to. If you need to pack a fragile item in luggage, avoid placing it in the same bag with a heavy item.
Whether in checked or carry-on luggage, high-alcohol-content liquids (e.g., liquor over 140 proof, major quantities of perfume/cologne) are deemed a fire hazard and will be confiscated if found.