When it is difficult to conduct a census of an entire population, a researcher will work with a portion of that population, a sample, which is thought to be representative of the population in question. Researchers typically try to ensure that a sample has been drawn in a random fashion. This ensures that the distribution of population characteristics corresponds to the assumptions of probability sample theory. This allows inferences to be drawn about the population. Many times non-random samples are used, however.
SAMPLING refers to the process or method of drawing a sample from a population. This process can be based on random selection such that each member of the population has an equal probability of being selected. Many statistical tests assume a process of random selection. However, the method may not be based on random selection. One might, for example, select for convenience the first 100 people you meet or all the students in an introductory sociology class.
Any sample is only one of many samples which could have been drawn from a population. Consequently, a researcher may not get the same results with each sample. As the sample gets larger this variation is less drastic, and the sampling error is smaller. Social scientists have ways of calculating the sampling error and you can see this in the news many times when a reporter says: a survey of this size is accurate within 3.5% 19 times out of 20. For example, the 3.5% is the sampling error. 95 times of 100 times the mean would fall within +/- the mean or average reported.
The actual physical representation of a population, a voters list or a student class lists, for example, from which a sample is actual drawn. A population is a somewhat abstract concept while the sampling frame is the real listing of members of that population such that you can imagine them being placed into a hat for purposes of random sampling.