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.
There are situations where it potentially fails -- for example, in cave deposits.
In this situation, the cave contents are younger than both the bedrock below the cave and the suspended roof above.
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.
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.
The simplest situation for a geologist is a "layer cake" succession of sedimentary or extrusive igneous rock units arranged in nearly horizontal layers.
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.
However, note that because of the "principle of cross-cutting relationships", careful examination of the contact between the cave infill and the surrounding rock will reveal the true relative age relationships, as will the "principle of inclusion" if fragments of the surrounding rock are found within the infill.