Satsuma is a style of Japanese earthenware that was produced in Satsuma, Osaka, Kyoto, Kobe, Kagoshima and Tokyo. Satsuma vases often come in pairs and are elaborately decorated with gold leaf and crackled glaze. Satsuma vases generally depict Japanese themes including scenes of court life, legends and artistic values. Dating Satsuma vases takes time and practice -- particularly if you're not familiar with the Japanese language -- as the bottom of Satsuma vases are marked with Japanese characters which indicate place names and/or a family crest.
Examine the mark on the bottom of the Satsuma vase. Oftentimes, Satsuma markings will have gold Japanese characters on a red background with a gold outline surrounding the red background; the entire marking may be in a square or rectangular shape. If the marking is rectangular in shape with a separate circular crest above the rectangle, the marking may indicate Gyokuzan, in which case the vase likely dates from 1868 to 1912 -- the Meiji period.
Consult a Japanese/English dictionary and a book on Satsuma markings. One such character indicates "bizan," which translates to "beautiful." A marking with a gold bizan character on a red background in a rectangular shape likely dates from 1912 to 1926, which is the Taisho period.
Look for a marking with gold Japanese characters on a black background in a square form, with gold lining the square. This marking may indicate that the vase was produced by the Kinkozan family; the Kinkozan family's primary production period was from 1875 to 1927.
Certain websites, such as gotheborg.com, have pictures of various Satsuma markings and details regarding dates and producers.
If the bottom of a vase is marked "Royal Satsuma," it is not an original Satsuma, as real Satsuma vases do not have English markings.