Check the price and the vendor. This is one of the easiest ways to tell if you're dealing with an original work of art. Original Remingtons are worth millions of dollars. Sotheby's, Christie's and other elite auction houses are often the entities that sell them. When someone sells an original Remington, it's usually a newsworthy event.
Look for the foundry mark. Original sculptures always possess an indication of where each was made, whereas reproductions rarely do.
Look at the base of the sculpture. A bronze base signifies an original, whereas a marble base is typical of a copy.
Check under the bronze base for a single number. Remington gave original sculptures single numbers in the sequence that he made them. On the other hand, several numbers such as "10/200" underneath the base are a sure sign of a fake.