How are confidence intervals calculated?

A 95% confidence interval is not so much a statement about any particular interval, such as (79.3, 80.7), but pertains to what would happen if a very large number of like intervals were to be constructed. That is, from a practical point of view, the 95% gives the fraction of the time, in repeated sampling, that the intervals constructed will contain the target parameter µ. How are confidence intervals calculated?