How does someone become a greek god, in other words, how did Zeus or Athena become a god or get the title "greek god"?

Gods (generally) do not become gods. They are gods. The Greeks used the myths of the gods and goddesses and their interaction with humans to explain the world around them, the origin of the world, to teach ethical lessons. It was their religion as Christianity, Judaism, and Buddhism are religions people believe in and practice the tenets of today.

They were considered gods because of the power they had. Their powers were by virtue of being the children of the titans.

Sotto voce: Many Roman Emperors were deified after their deaths.

@gailcalled Yeah, sort of like canonization.

yeh gotta be thunk up t’ ‘splain th’ sun rizun.