The representation theory of finite groups over the complex numbers is classical und it is usually quite easy to compute the set of isomorphism classes of irreducible representations, at least for small examples. Now, sometimes one is not content with the representation theory over the complex numbers or even over any field, but one wants to consider representations over $\mathbb{Z}$ or $\mathbb{Z}_{(p)}$. At least for the non-expert it is not so easy to obtain a complete list of isomorphism classes of indecomposable representations in these cases even for small examples. So, what I want to ask is the following:

1) Can one formulate a "guide" how to obtain such a list?

2) Is there a place in the literature where a list of indecomposables/irreducibles is given for some small examples as $S_3$ (the symmetric group on three elements)? In the last example I am especially interested.