Though Wedgwood makes pottery, it is not of the craftsman variety that the term "pottery" often indicates. Wedgwood vases are made of fine earthenware and fine bone china. Wedgwood's jasperware is the most famous and common material for their vases, with white figures (usually depicted in Greek- and Roman-influenced styles), on pale blue, pale green, yellow, taupe, brown or black backgrounds.
Given the stylistic diversity of Wedgwood vases, the best way to identify a Wedgwood vase is a painted or embossed mark on its bottom. These have changed somewhat over the years, but the most common examples read "Wedgwood Made in England," "Wedgwood England" or "Wedgwood of Etruria & Barlaston." You may also see a small drawing of an urn with "Wedgwood" printed underneath it.
Unmarked vases are unlikely to be Wedgwood unless they are quite old. If the quality of the vase leads you to believe it's of Wedgwood make, despite the lack of the mark, get the dealer or seller to provide proof (deeds of sale from over the years are one possibility).
Though there is a "Wedgewood" company -- Enoch Wedgewood of Tunstall -- their wares are not nearly the quality of those by Wedgwood. Any vase marked with "Wedgewood," spelled with an "E," is of little to no value to collectors. The Enoch Wedgewood of Tunstall company often marks their pottery with a unicorn.