This document is partly based on a prior posting composed in reply to Ted Holden.
My thanks to both him and other critics for motivating me.
Many other indicators are commonly present, including ones that can even tell you the angle of the depositional surface at the time ("geopetal structures"), "assuming" that gravity was "down" at the time, which isn't much of an assumption :-).
In more complicated situations, like in a mountain belt, there are often faults, folds, and other structural complications that have deformed and "chopped up" the original stratigraphy.
They are applied by geologists in the same sense that a "null hypothesis" is in statistics -- not necessarily correct, just testable.
In the last 200 or more years of their application, they are valid, but geologists do not assume they are.
In such a situation, the "principle of superposition" is easily applied, and the strata towards the bottom are older, those towards the top are younger.
Despite this, the "principle of cross cutting relationships" can be used to determine the sequence of deposition, folds, and faults based on their intersections -- if folds and faults deform or cut across the sedimentary layers and surfaces, then they obviously came after deposition of the sediments.
You can't deform a structure (e.g., bedding) that is not there yet!
As an example of how they are used, radiometric dates from geologically simple, fossiliferous Cretaceous rocks in western North America are compared to the geological time scale.
To get to that point, there is also a historical discussion and description of non-radiometric dating methods.