Add to the pot when making Thai Curry and for flavouring other stews and stockpots. The pieces should not be eaten, but removed before eating. If you wish, you can pop some into a muslin bag to make it easy to remove, rather like you would with a Bouquet Garni.
Galangal is usually combined with Lemongrass and Root Ginger to create an authentic Thai flavour. Galangal has a deep aromatic flavour that lends complexity to a sauce.