Download the code anywhere, open Magma, and type:
> load "path-to-file/DeRham.m";

Then type:
> R<x,t> := PolynomialRing(Rationals(),2);
> A := GaussManinMatrix(x^5+t);

This will give you the matrix of the action of d/dt in the family of projective curves defined by y^2 = x^5+t over the affine t-line.
Replace this by any polynomial P(x,t) in x and t (monic in x) you like, this will give you the Gauss-Manin connection for the family y^2 = P(x,t) over t. 

To get the residue matrix at t=0, type:
> ResidueMatrix(A);

To get the residue matrix at t=c, type:
> ResidueMatrix(A:z:=c);