The logit is a transformation of a variable. It is used in logistic regression, which is applied when the dependent variable is dichotomous -- has only two categories. Logistic regression models the probability of an event, such as voting for Barack Obama, based on independent variables, such as age, sex and income. But probabilities are always between "0" and "1," and regression methods expect the dependent variable to vary between negative and positive infinity. The logit transformation transforms probabilities so that they have this range.
Find the probability of an event. For example, the probability of a person voting for Obama might be 0.55.
Subtract this from 1. In the example, 1 - 0.55 = 0.45.
Divide the result in step 1 by the result in step 2. In the example, 0.55/0.45 = 1.22.
Take the natural logarithm of the result in step 3. In the example, ln(1.22) = 0.20. This is the logit. You can find the natural logarithm on many calculators.