Archaeological chronology aims to answer the question “When did this or that event happen?”. This question can usually be re-phrased as “When was this or that thing made?”, where the thing under study may be anything from a bead up to the Great Wall of China.
Most dating evidence is based upon similarity: people are almost incapable of doing anything in exactly the same way for any long stretch of time, and when they try to return to an old way of doing something, they never get all the details right. Such similarities (again on all scales of evidence) are dealt with in a more or less formalised way by means of a tool kit called typology. Collect a group of similar pots / house foundations / Great Walls, note explicitly the details that unite them and separate them from their peers, and you have a type definition. Thus defined, all types have a chronological delimitation, though many may be too long-lived to be very useful, and the presence of one type of pot doesn’t rule out the parallel existence of several other types.
The very birth of archaeology as a scientific discipline is reckoned from the first chronological and typological breakthrough: C.J. Thomsen’s 1821 division of Scandinavian Prehistory into three Ages where cutting tools were made of different materials. First stone, then bronze, and then iron. Chronological research is still working to sub-divide the three Ages into ever finer well-defined slices.
The definition of an archaeological period takes the form of a list of types found associated with each other: pots, houses etc. How can we know in what order these periods occurred? We still largely do this by typological seriation and stratigraphy.
Seriation is a more or less formalised process where you order a collection of pots / houses / Great Walls according to similarity. You put two pots on a table, grab a third pot and decide if it should go between the two or over to either side. This is formalised as pot 1 having traits ABC, pot 2 BCD and pot 3 CDE. Then test if the series you’ve established is chronological, firstly by seriation of closed find associations (graves, hoards) by the same means, then by stratigraphy. Are ABC pot sherds usually in layers located on top of separate layers with CDE pot sherds? Or the other way around? Or are they usually mixed up?
So far I’ve spoken only about relative chronology, where we can say with confidence that the types listed for period B fill the interval between periods A and C. What about absolute chronology, that allows us to say that the period B types appeared in the AD 10s and were replaced by period C types in the AD 150s? There are many methods, most importantly radiocarbon.
Radiocarbon dating is a complicated field of research that moves forward rapidly. Briefly put it will tell you when a certain living thing died. With current technology, the accuracy is usually counted in decades. Much of the intricacies with radiocarbon have to do with the relationship between the death of that living thing and the event an archaeologist wants to date. If you find a piece of charcoal on a settlement site, you first need to think about how it ended up there. Stratigraphy is paramount: is it under a stone foundation? Or is it in a ditch that cuts across a house foundation? If you can’t answer such questions, don’t even submit the sample. And you need to think of intrinsic age: the heartwood of an old oak died centuries before someone cut the tree down. A wood anatomist can judge this for you. Bones have no intrinsic age, but their apparent age is skewed by the amount of seafood the creature ate in life.
Other important absolute dating techniques are historical dating (e.g. coins with dates on them or the names of rulers whose regnal dates are known), dendrochronology (the width of tree rings varies with the weather, forming a chronological bar code) and thermoluminiscence (quartz in a brick or potsherd or hearth stone accumulates radiation energy after being set to zero by strong heat).
Techniques like radiocarbon have not made typology or stratigraphy obsolete. For one thing, you need robust typological definitions to be able to generalise the radiocarbon date of a single object to an entire group of similar ones. Furthermore, fashion changes at shorter intervals than the current accuracy of a radiocarbon date. This means that you can often get a tighter date from typology than from radiocarbon. Southern Scandinavia’s Migration Period lasted about 170 years and is thus about three radiocarbon dates long. But seriating a sample of female graves from Gotland, I managed to define four successive fashion phases for the same interval.
For a more thorough treatment of the subject, see Kris’s long post over at About.com.