You can determine the authenticity and value of a 1971 Eisenhower dollar using the About Coins guide to Eisenhower dollar value and prices. The website includes a guide to determining when a coin is from and how to judge its value.
Using the About Coins guide to Eisenhower (Ike) dollars, several possible values for a 1971 Eisenhower dollar can be determined. Based only on the year given, a 1971 Eisenhower dollar could have a sale value anywhere from $1.05 to $10.
This difference in price is wide, and determined largely by the mint of the coin and its condition as either circulated or uncirculated. The lowest sale value ($1.05) is that of a coin minted in Denver and circulated. The highest value ($10) is that of a coin minted in San Francisco, uncirculated, with silver Proof. Proof, which is always capitalized when used in reference to coins, refers to a type of finish used on collectible coins.
The location of a coin's mint can be determined by looking just below Eisenhower's neck for a small D or S called a mint mark, which indicates whether the coin was minted in Denver or San Francisco. It should be noted that although these factors contribute to the value of a coin, the actual sale amount of the coin is variable and based on any number of other factors.