What is the difference between 喝 and 饮?
饮 is more of a classical term which mostly exists in established words and phrases: 


As verb: 饮酒, 饮水思源，饮鸩止渴, 饮泣, 饮恨, etc.
As (part of) noun: 饮品, 饮料, 饮片, 饮具, 冷饮, 饮食, 饮用水, etc.


Use 喝 in everywhere else.

Usually you don't create words and phrases with 饮. I tried a few and they all sound funny:


饮可乐, 饮咖啡, 饮西北风, 饮汤 -- DON'T EVER USE THESE.