When butchering beef, the most important things are to only use very sharp knives and to work slowly and carefully for the best results. A boning knife is often the most effective because its thin shape allows better maneuverability. Short, careful strokes of the knife give the best accuracy and prevent accidental injury.
While trimming the beef, the best way to cut away fat and skin is to peel it slowly upward while gently cutting underneath. This method is slower than simply cutting excess away piece-by-piece, but the results are cleaner and save the most meat. With the largest fat deposits cut away, smaller pieces peel away easily by hand.
Taking time and being patient is very important when butchering beef to keep as much meat intact as possible while removing the most unwanted pieces. The most important part to cut away is the silver skin, the thin membrane of fat and sinew on the outside of the meat. The silver skin gives the beef a bitter taste if it's cooked.
Another tip is to reserve everything from the meat to make homemade beef stock. This includes the liquid drained from the package when opened and the fat and sinew cut away. These parts, when simmered in a pot with vegetables and seasoning for a few hours, strained and then frozen, are useful for future soup, stew or gravy.