My husband and I don't speak any Mandarin, but my children began studying at a Mandarin-immersion school more than 10 years ago. In an effort to help my children adjust to a Mandarin-speaking environment, I searched for ways to help introduce the language at home.
Ten years ago, I was unable to find anything on the internet, which is now one of the best sources for Chinese-learning tools. There are dozens of great videographers on youtube.com, who post frequent, short lessons. One of my kids' favorites is AskBenny.com. (See a short clip here: http://www.youtube.com/watch?v=FXxYpSC6yLk&feature=related).
Chineselessons.com is a great resource for learning pinyin and bopomofo. As I understand it, Pinyin is a writing method, which is romanization of Chinese characters. Bopomofo is used mainly in Taiwan as a system to teach pronunciation of Chinese characters. (Feel free to correct me if I have this wrong!)
For younger children, the web is a great resource for downloadable pages to reinforce character memorization. Gigglepotz.com will definitely be a younger child's favorite spot for learning Chinese, downloading pages and exploring new topics related to China. (Visit the site at: http://www.gigglepotz.com/china.htm)
A brush-painting set is a must for both younger and older children. Painting the Chinese characters is fun and great re-enforcement for memorization. My kids still love to practice new characters, as well as paint landscapes, with their brush painting sets. (Check out this link about brush painting: http://www.nanrae.com/lesson-pg1.html)
Some of the best sites for purchasing flash cards, workbooks, dvds, and other Chinese-learning tools are AsianParent.com, Childbook.com, AsiaForKids.com and Chinasprout.com. I find that giving my kids exposure to a variety of learning tools keeps their interest.