Answer:
The surest way to authenticate a coin is by submitting it to an authentication and grading service. They will authenticate your coin, assign a condition grade to it, then encapsulate it in a sealed container.
Other that that you can do this yourself by comparing the coins features with a similar coin that is established as authentic.
Coin authentication has become important since the coin collecting community has been flooded with high quality fakes from China. The quality of the fakes is so good that the only way to be sure of the authenticity is to have the coin professionally authenticated. The presence of these fakes also makes it necessary to know who you are buying from, on-line auctions or mail order are very risky and offer no fraud protection, I would recommend avoiding them.