Euler's Method approximates the solution of an ODE by using a step-by-step approach. Given a differential equation of the form dy/dx = f(x, y) and an initial condition y(x0) = y0, the method proceeds as follows: 1. Choose a step size, h. 2. Compute the next value: y(x0 + h) ≈ y0 + h * f(x0, y0). 3. Repeat the process for subsequent steps.