English "of" or 's is usually translated into Polish as Genitive case.

If you're asking when masculine genitive ends in -u and when in -a – there are very few rules, and they're full of exceptions. There are even homonyms with different meanings that differ only in genitive. I suggest simply remembering them and you may start intuitively grasping patterns.

http://lpj.pl/porada13.htm
http://www.ekorekta24.pl/aktualnosci-jezykowe/9-odmiana/165-dopelniacz-liczby-pojedynczej-rzeczownikow-rodzaju-meskiego-koncowka-a-czy-u