In other words, artifacts found in the upper layers of a site will have been deposited more recently than those found in the lower layers.
For example, since each Roman emperor had his own face stamped on coins during his realm, and dates for emperor's realms are known from historical records, the date a coin was minted may be discerned by identifying the emperor depicted.
For detailed information about how seriation works, see Seriation: A Step by Step Description.
Seriation is thought to be the first application of statistics in archaeology. The most famous seriation study was probably Deetz and Dethlefsen's study Death's Head, Cherub, Urn and Willow, on changing styles on gravestones in New England cemeteries.
Using local pine trees, Douglass built a 450 year record of the tree ring variability.
Clark Wissler, an anthropologist researching Native American groups in the Southwest, recognized the potential for such dating, and brought Douglass subfossil wood from puebloan ruins.
Many of the first efforts of archaeology grew out of historical documents--for example, Schliemann looked for Homer's Troy, and Layard went after the Biblical Ninevah--and within the context of a particular site, an object clearly associated with the site and stamped with a date or other identifying clue was perfectly useful. Outside of the context of a single site or society, a coin's date is useless.