A
Simple Random Sample (SRS) is the type of sample used almost
exclusively in
statistics. It involves identifying a
population (the
entire group of
individuals you wish to
report data on) giving each a
number, and then picking numbers randomly to create a
sample. Nowadays, picking
random numbers is generally done by
computers, but thats only
pseudorandom; if you want to be
hardcore,
RAND Corporation publishes a book entitled
One Million Random Digits containing (you guessed it) one million
random digits.
One important thing to note about an SRS is that while many people will define it as being a sample in which each individual from the population has an equal chance of being picked, this is only half of the definition; the more accurate definition is that every possible sample has an equal chance of being the sample.
To understand the difference, consider the following situation. Let's say you want to find out the mean weight of bowling balls. Bowling balls, in our imaginary world come in blue and red. 70% of all bowling balls in this world are red. The other 30% are blue. Picking 7 red balls and 3 blue balls does not make a simple random sample, even though each ball will get representation in the sample equal to its proportion of the population (this is a stratified random sample, actually). In a simple random sample, it would be possible (though unlikely) that you would get ten blue balls. This is the essence of a simple random sample - every possible sample has an equal chance of being the sample you pick.
A simple random sample is more or less the only type of sample permissible in most statistical calculations. This is also why you shouldn't trust statistics from call-in polls, standing-around-in-the-mall-asking-people-to-fill-out-a-survey polls, etc. - they're going to be very biased and unrepresentative of the population.