IIRC I learnt a lot from Katz' papers from the 1970s. Of course the basic construction is the same as the elliptic curve case: you take C^g, quotient out by the lattice coming from E via its g embeddings into C, and then you have to prove that the quotient is an abelian variety, which involves writing down a non-degenerate Riemann form. This isn't hard, but I think I first saw it in one of Katz' papers. Oh---I should say that before I read Katz I read the section on abelian varieties over C in Cornell-Silverman (although there will be other references for this stuff).