An algorithm to find isometry between surfaces in $\mathbb{R}^3$?

Question

Given two surfaces in $R^3$, i would like to find isometry between these two. Usually, in class, we did some examples, like bending the plane into a cylinder, or cone, and they were not hard, quite trivial, actually. I was wondering whether a more general algorithm exists, that, presuming surfaces are isometric, gives us, at least one isometry map between them. I know that surface isometry preserves first fundamental form, and was i thinking that it might help in the process, but i can't figure out the whole general algorithm on a more abstract level, and am only able to figure it out somehow, if i am given the surfaces already.