A true auction, well advertised and attended. Next best is to offer it to a dozen or so knowledgeable collectors who need it to fill a hole, and see how high one of them will go. The best practical method is researching auction results and averaging the several most recent.
The best?? The best way to determine what a coin is worth is through experience plus that would also qualify as the most reliable. Many, many people make the mistake of thinking that this (what a coin is worth) should be easy but like anything else in life it requires work and study. Can anyone come up with a subject that does not? The short answer is probably the truest but most unsettling - a coin is worth, (or a car, house or mule) what buying and seller agree upon. With that said the long answer is look at thousands of coins, read thousands of books, talk to thousands of collectors and dealers and then after 20 or 30 years you will have some experience needed to answer your own questions about what a coin is worth and come very close to the price that makes you happy. Now I know that is not what you are asking on here most likely and what you really may want to know is, "without doing all the above how can I find out what my coin is worth right now"? The answer to that is go to eBay and find out what similar coins are selling for. You will probably not be very surprised and not be able to quit your day job over this coins worth but I hope it's a good one! Ben Peters
Actually ebay is not a good source for accurate pricing. There are far too many buyers on ebay buying things that they have no idea what the real value is. And as a result they are vastly over-paying for the coins. Because of that ebay is a terrible source that should never be used as a price guide.
That depends on how lucky you are. ebay is much like a casino, sometimes you win and sometimes you don't.