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The scholar most associated with the rules of stratigraphy (or law of superposition) is probably the geologist Charles Lyell.
The basis for stratigraphy seems quite intuitive today, but its applications were no less than earth-shattering to archaeological theory.
Many of the first efforts of archaeology grew out of historical documents--for example, Schliemann looked for Homer's Troy, and Layard went after the Biblical Ninevah--and within the context of a particular site, an object clearly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.
And, outside of certain periods in our past, there simply were no chronologically dated objects, or the necessary depth and detail of history that would assist in chronologically dating civilizations.
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.
Cross-dating of sites, comparing geologic strata at one site with another location and extrapolating the relative ages in that manner, is still an important dating strategy used today, primarily when sites are far too old for absolute dates to have much meaning.
Using local pine trees, Douglass built a 450 year record of the tree ring variability.
Two broad categories of dating or chronometric techniques that archaeologists use are called relative and absolute dating.
Dendrochronology has been extended in the American southwest to 322 BC, by adding increasingly older archaeological samples to the record.
There are dendrochronological records for Europe and the Aegean, and the International Tree Ring Database has contributions from 21 different countries.
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.
Not only that, it varies regionally, such that all trees within a specific species and region will show the same relative growth during wet years and dry years.