How old is your baby? Speaking to your baby in "Motherese" ( infant-directed speech [IDS] or child-directed speech [CDS]) is probably what you're talking about, mothers talk to their babies in a specific pitch that seems to help them learn languages in a way that adults can't - adult brains arrange information in certain ways that are very different to the way that babies acquire L1 and L2 - so there's no such thing as "learning a second language the same way you learned your first" as a lot of courses (esp. Rosetta Stone and Wall Street Institute's courses) sell themselves on.
Also, babies brains appear to have the ability to isolate the phonemes of a language - babies and toddlers are able to produce all the sounds that every language uses, but somehow keeps the ones that are in the native language (and L2 if need be) and discards the ones that it doesn't need.
The general consensus seems to be that after the age of 13, the ability to learn and speak a language without a noticeable foreign accent rapidly decreases - Henry Kissinger came to the US after he was thirteen and has a characteristic accent, whereas his brother who is 2 or three years younger, speaks flawlessly with an American accent.
From Wikipedia: "research suggests that in a tonal language, such as Mandarin, the use of child directed speech is beneficial to development. Specifically, Mandarin features lexical tones that must be used with every syllable which in turn convey meaning. It has been seen that in tonal languages such as in this example mothers use child directed speech by heightening the pitch of speaking making the product easier for infants to understand."
I don't think that there's any good way to teach a baby a second language apart from actually directly addressing the infant in Mandarin and using Motherese if you can. The language centre of their brains behaves in a much different way than it does in adults. Steven Pinker's "The Language Instinct" has excellent coverage of how youngsters play around with grammatical patterns and vocabulary (in English) if you're interested in reading more on the subject, and Malcolm Gladwell covers "crib talk" in his book "Tipping Point".
Apologies for the dense, overlong reply, I've spent four or five years teaching English and am really quite geekily into language acquisition techniques and methodologies :P