Look underneath the image of the picture, if it has wording such as "reproduced by," "reprinted by" or "courtesy of," then it is not an original print.
Hold the picture at an angle, according to the Currier and Ives website. The prints were individually hand-colored before being available for purchase. Often, the artist used gum arabic on the colors, this varnish will have a sheen to it, and if the print is held at an angle the shine of the varnish will appear.
Examine the print under a magnifying glass. Reproductions will have the tiny dots of the print in a uniform pattern, often geometric or a dot with a semi-circle surrounding it. The authentic prints will have no uniformity under magnification.
Measure the print. Currier and Ives only printed three different sizes of folio, the small ones being 8 by 12.5 inches, the medium prints were 10 to 14 inches by 14 to 20 inches, the large folios measured over 14 by 20 inches. If your print does not fall into one of these groups, it is most likely a reproduction.
Contact an art curator or a specialist in rare art; they will be able to examine your print and tell whether it is authentic and what it is worth.