If it is made with large pieces of meat and potatoes
Brocho before eating the potatoes: Borei Pri Ha'adama
Brocho before eating the meat: Shehakol Niyeh Bedvoro
Brocho after eating the proper shiur of this: Borei Nefashos
If it is made with small pieces of meat and potatoes
If the meat is the majority, the Brocho to say before is: Shehakol Niyeh Bedvoro
If the potatoes are the majority, the Brocho to say before is: Borei Pri Ha'adama
Brocho after eating the proper shiur of this: Borei Nefashos
Source: The Laws of B'rachos (page 369)