Greek training is the training that Greek demigods are taught to survive. The campers at Camp Half-Blood use this training in battle and to become great warriors.
Greek training is about adapting an enemy's move and could quite often vary, depending on the threat faced. Unlike Roman training, which emphasises on "strength in numbers", Greek Training encourages practitioners to be assertive. It is about seeing what your opponent's next move is, then dealing with it, as shown when Percy said that he could tell what Ares' next move would be by the way his muscle tensed. However, conventional Greek military tactics, notably the phalanx, was also used (as in the Battle of the Labyrinth).
The Greek fighting style with a sword can be labeled as unorthodox, and unpredictable. It involves slashing, instead of stabbing like the Romans would. Therefore, Greeks are usually able to defeat multiple Romans. Rolling under someone legs, whacking with the flat of your blade, somersaulting, and feinting are all parts of Greek fighting style. Weapons used in Greek warfare are usually knives, swords, bow and arrow, circular shield, and spears.
After bathing in the River Styx, when Percy fought Hades' army of Skeleton Warriors, his Greek training mixed with his enhanced combat skills put his mind into "autopilot," allowing him to take down the whole group of warriors and pin Hades to the floor in seconds.
During the war games, Percy rolls under the defenders feet, slashes instead of stabbing like a Roman would, and whacking defenders with the flat of his blade, generally causing mass panic. When Percy is on the Hubbard Glacier, he uses his Greek fighting style to hold off a small army of continually resurrecting Roman ghosts, showing how effective this style is.