There are several techniques of this kind, but the method usually called controlled crying is the one also known as the Ferber technique. It was created by Dr Richard Ferber in the 1980s, but the basic idea of letting babies cry for a while until they go back to sleep is a very old one - many parents did the same thing in the past without having a name for it.
Of course, many parents don't like to use controlled crying at all, and would always go to a baby if it's crying. However, for those who use this method the usual advice is that you shouldn't try it with a baby under 6 months old. A major reason for this is that very young babies really should be checked if they cry, as at this age there is more likely to be something wrong or the baby may well be hungry.
So about 6 months is considered the right time to start, but the technique has to be used carefully - there are some very clear tips here to help you.