First to learn the Lagrangian Method, the principle of least action. According to the principle of least action, the path that a system will actually follow is the one that minimizes this action. This principle can be mathematically formulated as the Euler-Lagrange equation, which is given by:

∂L/∂q – d/dt (∂L/∂q̇) = 0

The detailed deducing of Euler-Lagranian equation is provided by Physics with Elliot.