You can try with Brown's book

[Cohomology of groups][1],

Chapter V, Section 6, p. 121 ("Application: calculation of the homology of an abelian group").


Maybe take also a look at the following papers by Baumslag, Dyer and Groves:

[The integral homology of finitely presented metabelian groups I][2]


Amer. Journal of Math. 104 (1982), 173-182



[The integral homology of finitely presented metabelian groups II][3]


Amer. Journal of Math. 109 (1987), 133-156

and at the references therin.


**EDIT.** J. Schafer's thesis

J. Schafer, On the homology ring of an abelian group, Dissertation, University of Chicago, Chicago, Ill., 1965

seems strictly related to what you are looking for. However, I could not find any published paper with this title. The only Shafer's paper related to homology of abelian groups seems to be

[J. Schafer: Abelian groups with a vanishing homology group][4]

Canad. J. Math. 21(1969), 406-409. 
 

   


  [1]: http://books.google.it/books?id=6x0mfOUFYgsC&printsec=frontcover&dq=brown+cohomology+of+groups&source=bl&ots=uwgXotQ-Vr&sig=dJ7UqQ1VGs00bMbb6MJB1i_xnk8&hl=it&ei=Kj4XTZbLMMmo8QPynrWFBw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q&f=false
  [2]: http://www.jstor.org/pss/2374072
  [3]: http://www.jstor.org/pss/2374555
  [4]: http://math.ca/cjm/v21/cjm1969v21.0406-0409.pdf