Using a solution manual effectively while studying challenging physics problems involves a strategic approach. It's beneficial to attempt problems independently for a set period, such as two hours, before seeking help. If progress stalls, taking a break can provide clarity. Waiting a few days before consulting the solution manual allows for deeper understanding and retention of concepts. This method promotes mastery of mechanics skills, especially when preparing for advanced courses like Analytical Mechanics. Engaging with high-level problems, such as those from MIT or Edward Purcell, can further enhance problem-solving abilities while self-studying topics like wave and optics.