When my son is young, he likes to read books with cartoons. Just let them read cartoons of Chinese famous book - like 'a journey to the West'. When he is familiar with the story, then buy the same story book but with more words. Because he already know the story, it will help him to read the words.
Like 'a journey to the West', bookshop has different books for different level of students.
When I read story books to my just-3-year-old girl, I pointed to the words and read. Of course, I will elaborate the stories with my own words by pointing the pictures. She seems quite get used to it and now she will demand me to point to the words to read to her when we get a new book (also for the old ones she read). Then, she will point to the words to read by herself. But I never check if she can recognise the words.