The central limit theorem gives a fundamental result for sampling - that large samples, or any samples from a Normally distributed population, are Normally distributed. Test this result to see that it really works. For this you can:
Use a spreadsheet to generate a population of random numbers
Draw a frequency distribution of the numbers and confirm that they follow a uniform distribution (where each number has the same probability)
Take large samples from this population of numbers and calculate the mean of each sample
Draw a frequency distribution of these means (i.e. the sampling distribution of the mean)
Confirm that the result is Normally distributed.
Now repeat this process for different sample sizes and initial distributions of values to see what effect this has.