Butter is a type of fat . The digestion of fats takes place in the following way :

In the buccal cavity and stomach. : Fats are not digested in buccal cavity and stomach. In stomach gastric juice has very weak gastric lipase which converts some fats into fatty acids and glycerol. This reaction is, however, negligible.

Digestion in duodenum : In duodenum the food is mixed in bile and pancreatic juice.

Role of bile : Bile emulsifies the fats and increases solubility of fatty products. The bile salts helps in the absorption of fats and fat soluble vitamins (A, D, E, K). 

Pancreatic juice : Fats are broken down by lipases present in the pancreatic juice and with the help of bile into di-and monoglycerides.

Digestion in Jejunum-ileum : In jejunum-ileum food is mixed with intestinal juice or succus entericus which has intestinal lipase which converts remaining fat into fatty acids and glycerol.