Incidence and prevalence are statistics widely used for reporting on diseases. "Incidence" is how quickly new cases are occurring; "prevalence" is how much of the population is affected. The calculations can be used for conditions other than medical reporting; for instance, we could talk about the prevalence of students dropping out of high school, or the incidence of getting a driver's license.
How to calculate incidence
Define the population at risk. This should be a group of subjects (e.g. people) who are currently affected.
Take a random sample from that population. This may be impossible to do precisely, which can lead to biases in the estimation of incidence.
Follow that sample for a given time.
Check the status of the sample periodically. A certain number will be affected over the course of time.
Calculate the subject years at risk. Essentially, this means: Each subject is at risk for a given time; add up these times and convert to years. That is subject years at risk.
Divide the number of subjects who got the condition by the subject years at risk. That is the estimate of the incidence rate.
How to calculate prevalence
Define the population. This should be the entire population, whether they have the condition or not.
Take a random sample of this population.
Find how many subjects in the sample have the condition.
Divide the number in step 3 by the number in step 2. This is the estimate of the prevalence.