The basic method of obtaining equations that fit your 3D surface is called least squares which is a statistical method that solves a system of equations for unknown coefficients in the equation that minimize the error between the given points and the coordinates calculated from the equation using the best fit coefficients.
You pick the equation, which very much depends on where the input data came from and what you want to do with the surface. Polynomials are often the equation type used. For example, there are special arrangements of polynomials in specific coordinate frames for fitting the shape of an optical surface. These are called Zernike Polynomials and they are widely used by Optical engineers and Structural Analysts.