Archaeology, or archeology, is the science of digging through other people's abandoned crap
in hopes of finding some food or useful object (no, that's probably homelessness, or freeganism) in order to figure out how, and if possible, when they lived. In all seriousness though, it is classed as subdiscipline of anthropology which studies the human past through its material remains.
In contrast with sensible construction workers, archaeologists use the smallest possible tools to move the largest possible amount of dirt. The crap that archaeology studies is usually buried under craploads of dirt. As a result, archaeology takes a crapload of time. Not only does it take a crapload of time, if you fail to find anything then you are effectively an extremely overeducated ditch-digger. And if you do find something, it's always a series of small walls.
Archaeologists excavate sites of previous human habitation, and sometimes piss off the locals by digging up their forebears' graves and shipping the cool stuff that was buried with them to a museum in Europe. This latter habit has lessened of late, and slightly more honor and respect are now paid to the neato bones and stuff that they find. In some cases, they move the museum to the dig site to make things easier.
Question: If Lucy was perhaps really an ancient ancestor of most humans alive today, shouldn't we all be really pissed at Richard Leakey et familias?
Anyway, we digress...
 The Trowel
The trowel is the archaeologist's most indispensable tool (besides his beard). Without him, his trowel is useless. Without his trowel, he is useless. Common uses for the trowel include:
- Trowel dueling
- Salad fork
- Back scratcher
- Cake knife
- Swatting flies
Digging for artifacts
Archaeologists carefully scrape through layers of accumulated dirt and other debris, sifting carefully through the material to find their precious artifacts. They carefully measure exact locations and depths, and carefully note varying layers as they dig down, in order to produce voluminous carefully written reports on what they have found. Then they carefully compare notes to form hypotheses about all manner of aspects of the lives and times of the people they are carefully investigating. The use of fire through the ages for cooking food and whatnot has left layers of charcoal that can be used to carefully date the remains with which they are carefully associated.
Yes, archaeologists work very carefully.
In the UK a popular TV programme Time Team has greatly increased the exposure of
archaeotainment archaeology. The team of about five regular members and sundry assistants/labourers is interpreted by Tony Robinson (who played Baldrick in the Blackadder comedies). They have three days to trash examine a site (Why three? - who knows) and pretty pictures are used extensively throughout the performance show to wow the viewers help the audience visualise the site as it once was.
The Indiana Jones series of movies have also aided in the popularity of archaeology, although real archaeology, sadly, involves fewer fights, chases, supernatural forces, or death-defying escapes. The 2008 TV series Bonekickers attempted to reach a happy medium between Indiana Jones style unrealistic action and realistic Time Team style "science". No, it didn't work.
There are some examples of real life archaeological bad-assery that helped popularize the field as well. Mortimer Wheeler is probably the most famous. He was a World War I veteran turned archaeologist, best known for his work on Roman Bronze and Iron Age sites, his appearances on "Animal, Vegetable, Mineral?" and for being a playboy. He also invented the Wheeler grid, which is still standard in the field today. (That's fancy-talk for digging squares along a line. Pretty bad-ass, huh?)
 Archaeological Theory
There are various different theoretical approaches through which archaeologists interpret the past. The various schools of thought within mainstream archaeology (as opposed to pseudoarchaeology) include:
The culture-history approach essentially formed the basis for modern archaeology. It is defined by the grouping of various site and artefact types into different 'cultures'. While the approach acts as a fairly decent 'rule of thumb', the fact that such artefacts were often traded extensively means that this method of analysis risks oversimplification. The Marxist archaeologist, V. Gordon Childe, is generally associated with this approach. Culture-history has generally been superseded in the west by processual and post-processual archaeology. However, it remains influential in areas comprising the former Soviet Union.
 Processual archaeology
Processual archaeology, sometimes referred to as 'the new archaeology' is generally considered a reductionist methodology. The movement grew out of the United States, and is strongly associated with Lewis Binford and his students. Processualists wished to adopt a more scientific approach to archaeology and the aims of the movement were outlined by Binford in a paper entitled 'Archaeology as anthropology'. Processualism borrows the ideas of hypothesis and the scientific method from the natural sciences.
 Post-processual archaeology
Post-processual archaeology is the more interpretative approach to archaeological theory. It grew out of post-modernism in the 1980's. Post-processualism criticises the detached approach of processual archaeology, claiming that each individual interpretes the past in his or her own way and that an exact scientific approach to archaeology is virtually impossible. Ian Hodder, one of the foremost advocates of the post-processualism is known for encouraging his students and staff to formulate their own interpretations of archaeological finds. Post-processualism is currently the dominant approach in western archaeology, though processualism retains many staunch adherents.