What is the best way to teach a child Mandarin?
It would be worthwhile for you to read over what people say in this question: Would it be bad to only speak to a child in a language in which you are not completely fluent?

It raises some interesting points.

The top answer from Javid Jamae provides the following points:


Spend as much time as you can around native speakers (family, friends, church, temple, cultural organizations, etc.)
Make a concerted effort to improve your language skills by learning vocabulary that is pertinent to common dialog you have with your children (focus on commands, household objects, animals, etc.)
Keep a notebook near you and every time you can't remember a word you want to use with your child, write it down. Go ahead and use the English (or other language) word so you can complete your thought with your child. Then, after you learn the Mandarin word, make sure you use it from them on.
Find a list of most commonly used conversational words in Mandarin and make sure you know the first 300-500.
Put your child in language classes as soon as they're old enough (5-6 yo).
Play "What is this?" with your child. Point to things and have your child tell you what they are. Using flashcards works well too. I'm sure you can buy Chinese flashcards online. 
Get some Chinese-language kids TV shows and cartoons that you can play for you child when he gets a little older. 
Make a commitment to your spouse that you will only speak Mandarin in front of your child. Struggle through it and you guys will notice that you're getting better.