Historically, there have been several ways in which people practiced archaeology, in both therms of method as well as purpose and interpretation of results. The way discipline was shaped often depended on historical conditions.
Archaeology as a discipline developed during 19th century. It developed soon after the advancement of geology, which proved Earth was billions rather than thousands of years old, as was then commonly believed. Charles Darwin's „The Origin of Species“ eventually leading scientists to believe that humanity was in fact millions of years old, thereby providing a time limit within which the burgeoning archaeological movement could study.
The first approach to archaeological theory, practiced in late 19th and early to mid 20th century was cultural-history archaeology.
This approach was very object (artifact) oriented, and it's the main reason common people associate archaeology with „artifact hunt“. But even then it wasn't really about finding artifacts, but humans behind them. Cultural-history archaeologists believed that each human group has its own distinctive material culture, and that by observing typology and style of artifacts we can trace past peoples. They also believed cultures can influence each other and that artifact designs and types can move from culture to culture through trade, migration or invasion.
This approach proved to be problematic, because it meant that societies change their material culture only when somebody else influences them (without an explanation on how first inventions were possible). Also, linking material culture with human groups is not the best way of interpreting things, and it proved itself to be very dangerous. There were several examples of archaeological finds to be used for contemporary ideology and political needs, Germany during late 30s and World War II being just one of the most extreme examples.
The approach changed in the 60s, when archaeologists like Lewis Binford rebelled (in true sense of the word!) against cultural-history archaeology and proposed a more scientific way of practicing archaeology.
This new approach, called „New“ or „processual“ archaeology, required rigor scientific method, hypothesis formation and deduction. Processual archaeology treated culture as a system and the focus was often on adaptation to environmental conditions.
Archaeologists analyzed the way past humans organized their societies, how they used natural resources (such as food and minerals) and how adapted to change in conditions. This approach valued scientific method and almost treated archaeology as hard science. The goal was to be objective and, through research, reveal what past really was.
But after a few decades this approach was challenged by archaeologists such as Ian Hodder, Michael Shanks and Christopher Tilley in the 1980s. Being influenced by postmodernism, they developed post-processual archaeology, which was a reaction to rigid scientific method of processual archaeology. They felt treating human societies using scientific methodology had many disadvantages, so they developed an approach that focused more on individuals within past societies.
Post-processual archaeology also stress that there is no objective science- researches are always influenced by their own culture and their individual experience.
In that scene, post-processual archaeologists focus on reflexivity (being aware of one's own position relative to the material) and multivocality (accepting multiple interpretations and approaches as being complementary in understanding archaeological material). In this sense, there is no one, „right“ archaeological interpretation, just like there was no one objective past: each author has her or his interpretation just like each individual in the past had her or his idea of culture.
It is important to understand these three major schools were developed in different times, and while they criticize each other, none of them (not even cultural-history approach) is not completely abandoned. Archaeologists decide on individual basis which theoretical approach they want to adopt, and in many cases they opt for a combination of several theoretical approaches.