it's very simple: your category will have one object, S. the morphisms of S will be the functions Lz:S-->S defined by Lz(x) = zx (we get one morphism for each element of S).
1. morphisms are composable: for each pair of morphisms, Lz,Ly we have:
LzoLy(x) = Lz(Ly(x)) = Lz(yx) = z(yx) = (zy)x = Lzy(x) (since * is associative), for every x in S.
thus LzoLy = Lzy.
2. since 1 is an identity for S, we have the morphism L1(x) = 1x = x. it is clear that L1oLz = Lz = LzoL1.
3. composition is associative (obvious).
that's it...now we have a category.