Giclee is a digital print of extremely high quality. The French word "giclee" means simply a spray, referring to the spray of the ink onto the surface of the print. The giclees are typically made on special printers that use archival inks, and they can use as many as a dozen ink tanks of varying color, producing a range and depth of color definition not found in other print processes. Because the print is from a digital source, anything that can be made into a digital image can be printed. Because the giclees are archival, they are often used to reproduce work by artists.
Examine what the image is on, and identify whether it is paper, canvas or other fabric. Look for the grain of the material. Giclees can be printed on surfaces such as canvas as well as paper (basically, anything that you can run through a printer that absorbs ink), and they are commonly used to reproduce paintings on canvas. With a giclee, the image will appear to be seeped into the canvas. If you are looking at a high quality print on a prepared canvas surface (gesso) or fabric, there's a good chance it is giclee.
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Consider the characteristics of the image. If it is on paper--yet it appears to be a painting, complete with brushstrokes or marks of a palette knife--it's probably a giclee. The colors and tones of a traditional painting can be reproduced with extreme accuracy by the giclee process, yielding what is essentially a picture of a painting.
Texture to paintings reproduced by giclee can be added by hand as highlights, but they will be few. If the image is photographic on paper, it is harder to tell. A high quality giclee can look as detailed as a photographic silver print.
Look at the surface of the print with a magnifying glass for half-tone dots or similar tell-tale marks. If you see them, it is not giclee. It's likely an offset or other kind of mechanical print. What will set a giclee apart is the continuity of tone and the absence of half-tone dots or disintegration of the image under magnification. Because the ink jet is applied in microscopic droplets, the changes in tones and colors will be absolutely smooth, as in a photograph. (Giclees are sometimes used to make editions or salable reproductions of art photographs.) Look for gradual and unblemished transitions of color and tone.