Find the partial derivatives with respect to x, y and z of the surface's equation. For example, given the equation z^2 + 2xy - 3y^2 = 4, fx = 2y, fy = 2x - 6y and fz = 2z, where fx, fy and fz are the partial derivatives with respect to x, y and z, respectively.
Evaluate each of the partial derivatives for the point where the plane is tangent. For example, given the point (-1, 0, 2), fx = 2*0 = 0, fy = 2*(-1) - 6*0 = -2 and fz = 2*2 = 4. These values also correspond to the gradient vector at the given point: (0, -2, 4).
Plug the values into the formula fx*(x - h) + fy*(y - k) + fz*(z - l) = 0, where h, k and l are the coordinates of the given point. For example, 0*(x - (-1)) + -2*(y - 0) + 4*(z - 2) = 0. That simplifies to z = y/2 + 2.