To safely increase the intensity of workouts, individuals should implement gradual progression by manipulating various factors such as resistance, volume, and duration. Aim to increase intensity by no more than 10% per week to minimize the risk of injury. Incorporating methods like interval training or adding additional sets and repetitions can be effective, along with diversifying exercise types. Monitoring how the body responds to increased intensity, paying attention to any signs of fatigue or discomfort, is vital for ensuring a safe and effective progression in fitness routines.