Survival time is a term used by statisticians for any kind of time-to-event data, not just survival. For example, it could be time-to-graduation for students or time-to-divorce for married couples. The key thing about variables like this is that they're censored; in other words, you usually don't have complete information. By far the most common type of censoring is "right-censoring." This occurs when the event in question doesn't happen to all the subjects in your sample. For example, if you're tracking students, not all will graduate before your study ends. You won't be able to tell if or when they'll graduate.
List the survival time of all the subjects in your sample. For example, if you have five students (in a real study, you'd have more) and their times to graduation were 3 years, 4 years (so far), 4.5 years, 3.5 years and 7 years (so far), write down the times: 3, 4, 4.5, 3.5, 7.
Put a plus sign (or other mark) next to any times that are right-censored (that is, those that have not had the event happen yet). Your list would look like this: 3, 4+, 4.5, 3.5, 7+.
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Determine if more than half the data is censored. To do this, divide the number of subjects with plus signs (censored data) by the total number of subjects. If this is more than 0.5, the median doesn't exist. In the example, 2 subjects out of 5 have censored data. That's less than half, so the median exists.
Sort the survival times from shortest to longest. Using the example, they'd be sorted like this: 3, 3.5, 4, 4.5, 7.
Divide the number of subjects by 2, and round down. In the example 5 ÷ 2 = 2.5 and rounding down gives 2.
Find the first-ordered survival time that is greater than this number. This is the median survival time. In the example, 4 is the first number that is greater than two other numbers; this is the median survival time.
If you were doing this in a real study, you would probably use statistical software, such as R, SAS, SPSS or another program, to do this for you.