Classical, Simple, Complex, Lie superalgebras and Complex, Affine, Kac-Moody algebras and Complex, Kac-Moody Lie superalgebras have an associated graph -up to isomorphism- in the sense of a generalized Dynkin diagram :
Apart from the classical references (i.e. the articles of Kac and the dictionary on Lie superalgebras) which have already been mentioned in the preceding answers, an invaluable -imo- reference is the 3rd volume of J.F. Cornwell, Group Theory in Physics. Volume III: Supersymmetries and Infinite-Dimensional Algebras.
This book is maybe not so well known in the pure mathematics literature -it comes from the mathematical physics ... culture- but it contains an extreme wealth of detailed computations and examples, keeping at the same time a complete and rigorous presentation of the theory:
The classification of fin dim Classical, Simple, Complex, Lie superalgebras is presented in ch. 25 and detailed info on basis elements, dual spaces, roots, generalized dynkin diagrams, bilinear forms, matrix realizations etc is presented in Appendix M.
The same stuff but for Complex, Affine, Kac-Moody algebras and Complex, Kac-Moody Lie superalgebras is presented in ch. 26 and Appendix N. (however, the generalized dynkin diagrams are missing for the Kac-Moody Lie superalgebras case - there are just some hints and tips in p. 337).