The European style, also called the continental style, is to hold the fork in the left hand and the knife in the right. Once a bite-sized piece of food has been cut, it is conducted straight to the mouth by the left hand. The tines remain pointing down.
The knife and fork are both held with the handle running along the palm and extending out to be held by thumb and forefinger. This style is sometimes called "hidden handle" because the palm conceals the handle.
In the American style, also called the zig-zag method, the knife is initially held in the right hand and the fork in the left. Holding food to the plate with the fork tines-down, a single bite-sized piece is cut with the knife. The knife is then set down on the plate, the fork transferred from the left hand to the right hand, and the food is brought to the mouth for consumption. The fork is then transferred back to the left hand and the knife is picked up with the right. In contrast to the European hidden handle grip, in the American style the fork is held much like a spoon or pen once it is transferred to the right hand to convey food to the mouth.