The Way of the Spider is a martial arts style developed by Spider-Man and Shang-Chi as a way for Spider-Man to compensate for the loss of his Spider-Sense.
During Spider-Island, Spider-Man went to Shang-Chi for martial arts training on the recommendation from the new Madame Web to compensate for the loss of his Spider-Sense. Together they created the Way of the Spider, a modified version of Peter's own combat style and Shang-Chi's martial arts.
Peter Parker combined his bullying experiences, his superhuman capabilities, concepts from Captain America's Fighting Form, and his training from Shang-Chi to create it. He also increased his skill with it using his now returned Spider-Sense. He also combined his mastery of acrobatics into the Way of the Spider. He uses this fighting style to counter all types of combatants and it complements to his superhuman powers.