(for ice cream eaten alone see Ice Cream)
Brocho before eating the ice cream: Shehakol Niyeh Bedvoro
Brocho before eating the cone: If the cone is tasteless and only used to hold the ice cream, no Brocho is recited on the cone. However, if the cone contributes taste (like in the case of a sugar cone) the correct Brocho on the cone is Borei Minei Mezonos
Brocho after eating the proper shiur of this: generally Borei Nefashos. However, if a Mezonos was said on the cone (see above), and a proper shiur of the cone is consumed, an Al Hamichya would be required.
Source: The Laws of B'rachos (pages 223, 370)