fibre product with a scheme in terms of its glueing data

Question

So heres the situation. Let S be a scheme. Imagine you have two S-schemes X,Y with restrictions U,V respectively that are glued via a homeomorphism $f:U\cong V$. lets call the sheaf we obtain by this procedure Z. Now if we consider another S-scheme P. Is it then possible to describe $Z\times_S P$ in terms of the glueing data? For simplicity its fine if we assume S and P to be affine and Z to be a vectorbundle on S with trivial cover X,Y. I hope its clear what i mean here, if not please ask for clarification. A reference would be also greatly appreciated! Thanks for the help:)