"Gosto" gosta" and "gostam" forces "de" after them. "De" also implys when saying some thing like strawberry juice for example "suco de morango".
I'm sure I'm leaving out something or got something wrong but I hope I helped :-)
As a portuguese speaker, I can surely tell you that there are no rules to use 'de'. You will learn that some words require 'de', and you will have to know them.
It is not so hard, you can easily learn.