There are several methods, depending on whether you are dealing with a large group of horses or a single mare and foal. The traditional method is to move the mare(s) into a distant paddock so that the foal, or foals, cannot see or hear them.
PROS: Foals remain with their buddies in a familiar pasture and after a couple of days will realize they will not perish without their mothers.
CONS: This generally results in a lot of whinnying and running, which is stressful for both the foal (and the owner) and carries the potential for injury. This is not recommended for weaning a single foal, unless he has some trusted, gentle pasture-mates to keep him company.