Genyjo found Goku one day while walking through the mountains because a voice kept calling out for him. When Genjyo could not take it anymore, he went to search for the source of the voice. And finally he came to a cave that resembled a jail and sitting inside was Goku. Genjyo remembered his teacher's words about being the sun of someone else's life and that moved him to take in Goku at the temple where he lived. Though he acts like he doesn't care, he is extremely attached to the little monkey and gets angry when Goku is in danger. The same goes for Goku who worships Genjyo. In the original story, Goku was supposed to be Sanzo's errant disciple.
Interesting isn't it?
Later, Gojyo encountered Genjyo Sanzo (Sanzang) and Son Goku (Sun Wukong) when they were looking for Hakkai, who had murdered a thousand youkai and half a human village, and somehow the four ended up as the motley group heading West to Tenjiku today. He still remains close friends with Hakkai, because they lived together for nearly two years. Enough so that Gojyo/Hakkai or Hakkai/Gojyo (58/85) remain two of the popular pairings in the fandom. http://en.wikipedia.org/wiki/Sha_Gojyo_%28Saiyuki%29 Ha! Take that Nat!