Besides the British, Canadians, Indians, Free French, etc., who fought in Italy, Africa, the Pacific, and on the Western Front with the US, there were other, smaller, contingents from countries such as Brazil and Mexico. How can I find out about their experiences? Any books out there anyone can recommend?
There has been relatively little written in English about the experiences of the Brazilian and Mexican contingents in WWII.
However, this should get you started and if you happen to be able to read Portuguese or Spanish, check the bibliographies of these books for primary and secondary sources in their original language. :)
"The Forca Expedicionaria Brasileira in the Italian Campaign, 1944-45" in Army History 26: 1-11 (Spring 1993) by Frank D. McCann. It can be found online for free here.
The Brazilian Expeditionary Force, By Its Commander by Joaio Baptista Mascarenhas de Moraes.
Brazilian Expeditionary Force in World War II by Cesar Maximiano and Ricardo Bonalume. This short volume out of the Men-At-Arms series from Osprey Publishing is perhaps the easiest and most engaging introduction to the BEF.
The Mexican participation in the war was far smaller than the Brazilian. However, I quite enjoyed chapter 17 in Latin America's Wars: The Age of the Professional Soldier, 1900-2001 by Robert L. Scheina which deals with both Brazil and Mexico in WWII. It's worth a look if you can borrow a copy somewhere.