Sampling is important in social science research because it helps you to generalize to the population of interest and ensure high external validity. Since it is often impossible and not practical to enroll the entire population in your study researchers select a sample. Choosing a 'correct' sample means making sure that your sample is large enough and representative of the population.
One way to make sure that your sample is able to be confidently generalized to the population is to use a sampling model using either non-probability or probability sampling. Generally there are no right or wrong approaches to sampling but it is important to understand the strengths and limitations of each approach.
Probability sampling is the best way to ensure your sample is similar to your population since you are randomly selecting participants and all participants have an equal chance of being selected. Probability sampling includes Simple Random sample; Systematic sample; Stratified Sample; and Cluster Random sample. Probability sampling has some limitations because it can be time consuming, costly, and often not practical to be able to recruit participants this way.
Simple Random Sample – get a list of all eligible in your population; generate random numbers, and select subjects based on numbers generated (usually will use a random number calculator or chart).
Systematic Random Sample – same as simple random sample but here you will pick your own number. (Ex: Pick every 4th person who enters the cafeteria.)
Stratified Random Sample – the population is separated (stratified or strata) into groups that are randomly assigned (ex: undergrads and grad student).
Cluster Random sample - the population is separated into clusters and then participants are randomly assigned (ex: geographic regions).
Non-probability sampling is non-random sampling. Non-probability sampling's strength is the fact that it is usually easier and faster to collect your sample using these methods as compared to probability sampling. One of the main limitations in non-probability sampling is the fact that its not randomized and therefore your sample may not be truly representing your population.
Quota sample - sampling based on pre-determined quotas such as 60% women and 40% men.
Convenient sample - enroll people that are easy to find or 'convenient.'
Purposive sample (judgmental sample) - sampling of pre-determined groups such as white males aged 30-45.
Snowball sample - those already enrolled refer others to enroll in your research.
For additional information or to dig deeper into the topic of sampling I have included a link to the Social Research Methods book sampling page.
I hope this helps bring clarity to the ideas of social science research sampling methods and some of the strengths and limitations to each approach.