A simple random sample is obtained by choosing individuals in search a way that each individual in the population has an equal chance of being selected.
A simple random sample is free from sampling bias. However, using a random number table to choose the elementary units can be cumbersome, and sampling can be simplified by selecting say every 10th or 100th unit after the first unit has been chosen randomly. such a procedure is called systematic random sampling.
A systematic random sample is obtained by selecting one unit on a random basis and choosing additional elementary units at evenly spaced intervals until the desired number of units is obtained. For example, there are 100 students in your class. You want a sample of 20 from these 100 and you have their names listed on a piece of paper may be in an alphabetical order. If you choose to use systematic random sampling, divide 100 by 20, you will get 5. Randomly select any number between 1 and five. Suppose the number you have picked is 4, that will be your starting number. So student number 4 has been selected. From there you will select every 5th name until you reach the last one, number one hundred. You will end up with 20 selected students.
A stratified sample is obtained by independently selecting a separate simple random sample from each population stratum. Here is a great example
A cluster sample is obtained by selecting clusters from the population on the basis of simple random sampling. The sample comprises a census of each random cluster selected. For example, a cluster may be some thing like a village or a school, a state. So you decide all the elementary schools in New York State are clusters. You want 20 schools selected. You can use simple or systematic random sampling to select the schools, then every school selected becomes a cluster. If you interest is to interview teachers on thei opinion of some new program which has been introduced, then all the teachers in a cluster must be interviewed. Though very economical cluster sampling is very susceptible to sampling bias. Like for the above case, you are likely to get similar responses from teachers in one school due to the fact that they interact with one another.