A Fenton glass vase is identified by a manufacturer's mark or label found on the bottom of the piece. Once located, it's a matter of matching the symbols using reference books or online sources. The Fenton Art Glass website lists the logos and labels used between 1921 and 2005.
In addition to the traditional logos and labels, Fenton also used special marks for "seconds." In the glass industry, a second is an inferior piece that is sold at a discount. During the early 1990s, Fenton used a flame marking for seconds. Pieces sold in the Fenton Gift Shop were also marked with a solid or open star. Two stars were added on pieces donated for fundraising events. In 1998, the star was replaced with a simple "F" for gift shop pieces.
Since Fenton has been producing glass since 1905, your vase may be missing its label, or it may be faded. If made before 1921, your vase may not have the etched logo. If you have a general idea of the age of the vase, you may be able to identify it using Fenton glass identification books. Most of these references list their glass pieces by manufacturing date and have plenty of photos.