Open the Settings Application, Select General
Select Add New Keyboard
Select Chinese Simplified Pinyin
Typing Chinese using Pinyin
Tap or tap and hold the globe icon on the keyboard to switch between English and Chinese.
Type in Pinyin, and select the Correct Chinese characters.
Another fun input method uses handwriting recognition. Be aware that it primarily works by stroke-order and stroke direction. If you draw a character that is visually very close to the character you want, but don't use the correct stroke-order, it may not understand.
To install it, follow the steps above but add the Chinese Simplified - Handwriting keyboard.