I just realized that. Silly me. I had actually gone through the web high and low to look for such feature and ended up with some PinYin Free app. Very inconvenient.
Now, with this original built-in Chinese input feature (I'm sure I hadn't updated OS), I can easily switch keyboard to pinyin or even handwriting mode.
Settings -> General -> Keyboard
Perhaps I could do Hebrew and Greek soon after I've mastered the language.