Determine what, if anything, the artist is representing on the vase. If you observe only abstract elements, whether simple black brush strokes or complex triangular figures, you are probably looking at a pre-Geometric or Geometric work, dating anywhere from the 11th to the eighth century B.C. If instead you find vaguely human images, you are looking at an example of either Archaic or Classical Greek pottery, from the seventh to the fourth centuries B.C.
Look for animal motifs, checkered bands and other decorative elements on both the top and bottom of the vase. These examples of what scholars call "Orientalizing style" usually indicate that cultures from Asia Minor have influenced the artist, which means that the work probably dates from the eighth or seventh centuries B.C., when increased trade between Corinth, Syria and Phoenicia brought Greek artists into contact with these design principles.
Note the color of the figures. Silhouettes featured prominently in the Archaic pottery of the seventh, sixth and fifth centuries B.C. Toward the end of the sixth century, red figures began to appear. Around the same time, artists began to experience with polychromy, the use of multiple colors, often setting figures against white surfaces.