The most basic (though not necessarily easiest or most accurate) way to measure population is simply to count everyone. This is known as a census and is usually undertaken by government officials. In the past, religious organizations carried out censuses, but usually on a local or regional level. The Roman Empire conducted censuses in order to measure the pool of military-age men and for taxation purposes, but these were limited because Romans had to report to government officials in their hometown to be counted. People who were poor or otherwise unable to travel were seldom counted [source: Weinstein & Pillai]. The U.S. government conducted the first true census in 1790 and has conducted a full census every 10 years ever since. A full census is sometimes known as complete enumeration -- every single person is counted either through face-to-face interviews or through questionnaires. There are no estimates.
Even a full census has limits. In countries with very remote areas, it can be impossible for census takers to count everyone. The 1980 U.S. census suffered from a documented undercount in part because census takers were afraid to go into some inner-city neighborhoods [source: Weinstein & Pillai]. A census also has trouble collecting information on rare populations. A rare population is one that is small or not reflected in standard census data. The United States isn't allowed to collect religious information in the national census, for example, so American Muslims could be considered a rare population. People who participate in a particular hobby or own a certain model of car are other examples of rare populations.
One alternative to a complete enumeration census is sampling. You might be familiar with this as the method used by market research companies and political analysts to conduct their research. Statisticians use a mathematical formula to determine the minimum number of people who must be counted to constitute a representative sample of the total population. For example, if the total population is 1,000 people, researchers might only need to survey 150 of them directly. Then they can take the data from the sample and extrapolate it to the full population. If 10 percent of the people in the sample are left-handed, it can be assumed that 100 out of a population of 1,000 are left-handed.
Sampling can actually return more accurate results than full enumeration, but there are some caveats. All samples have a margin of error, because there's always a chance that the sample selected for the survey differs from the total population in some way. This is expressed as a percentage of possible variation, such as "plus or minus four percent." The larger the sample size, the lower the margin of error. In addition, samples must be chosen as randomly as possible. This can be harder than it sounds. Let's say you want to survey a sample of everyone in France. One method used in the past was to select names at random from the phone book. However, this eliminates certain classes of people from the possibility of being selected for the sample: poor people with no phones; people who use cell phones and thus don't appear in the phone book; people with unlisted numbers; and most college students.
Gathering population data for places that don't conduct censuses, or from historical periods before censuses became common, is accomplished by piecing together whatever demographic information is available. There may be partial censuses, local population data or information gathered by church or civic groups. Examining birth and death records provides other clues.