Research the company ahead of time. Auctions on board are not run by the cruise line but by outside contractors. A quick Internet search should bring up the company employed on your cruise and you can look into what sorts of merchandise they carry.
Know what you want before you go. If you are interested in a certain artist, knowing what prints of her work go for before you board will help you decide if the auctioneer's price is fair. If you see something at an early auction that you are interested in, consider spending some time using the ship's Internet service to check out current values before the next auction.
Watch the activity list to see when the auctions will be held. Depending on the length of your cruise there may be several auctions scheduled. Try to make the first one available to get a feel for the process before deciding if and what to buy.
Read any documents you are asked to sign! Depending on the company you may have to just give your name and cabin number to enter the auction or you may be asked to sign something more complex. Some might offer a credit account with them, but be wary of this tactic. Still, if you think you might buy, consider the terms and use your best judgment.
Attend the pre-auction viewings whenever possible. Unlike mainland auctions, these auctions will not feature a catalog for each event and many of the pieces they have on board may never be shown. At the viewing you will have the opportunity to anonymously request items to be included in that day's auction (they'll give you sticky notes to flag items with, for instance).
Ask the auctioneer or his assistant about any pieces that you are particularly interested in. Many times they will not only tell you the auction starting price, but also a lower, pre-arranged selling price that, if you agree to it, will essentially bypass the main auction process. Your selection will be featured early in the show, will be announced as pre-sold; you will raise your card and he will close the bidding.
Understand that what you are buying is seldom an original piece of art, more often it will be a print. These lithographs or serigraphs are still limited runs and may be embellished, adding to their value, but still not an original work of art. The exceptions are the memorabilia auctions which come with their own registered authenticity process.
Buy only pieces you like, you can afford and you will not regret later. Do not look at these purchases as investment opportunities regardless of what the auctioneer may say: value depends on demand and demand is very tough to predict.