The trick is to have very cold butter, and slightly simmering liquid. You put the cold butter in the simmering sauce and stir rapidly. This melts the butter without splitting it from the liquid. You end up with an onctuous, lustruous sauce.

Typically you would use about 30 g (1 tbsp) of butter for about 125 ml (1/2 cup) of sauce, but quantities vary.

Adding a dash of cream to your sauce before adding the butter will help avoiding the butter splitting.