What are some of the advantages of teaching my child baby sign language?

The main advantage that appeals to everyone is the lack of frustration your baby will experience if they are able to communicate his/her needs to you.  This, obviously, leads to less frustration on the parents’ part as well, not having to play a guessing game with their baby.  One story we always share with people is when Laura’s daughter was ten months old she was eating Cheerios and signing ‘more’. Laura would give her more and she would throw them on the floor and sign ‘more’ again. Laura said to her, “Then you don’t want MORE… what do you want?” Fireese looked at her and signed ‘more cheese’. She was amazed for two reasons: 1. Fireese put together a two word sentence at ten months. 2. There was no cheese in sight. Laura hadn’t offered her cheese during that snack time yet she was able to clearly communicate to her what she wanted. Imagine how frustrated she would have been if she hadn’t been able to tell me what she wanted.
There are other benefits to signing with babies.  Generally, the first words babies tend to speak are the words they already know the signs for.  This is partly because we repeat those words more than other words as we are reinforcing the sign. We tend so spend more time with our babies when we are reading stories and playing games simply because, again, we are repeating words more to reinforce the sign, therefore taking longer to get through an activity.  For example, when you read a book you may say a word once or maybe twice if you ask the child to point to the picture of the word.  However, when you are signing with the child you may repeat the word 5 or 6 times.  You may say something like, “bear, do you see the bear?  Do you know the sign for bear?  This is the sign bear.  Can you make the sign for ‘bear’?  Let me help you make the sign ‘bear’.”  In this example you’ve said the word ‘bear’ six times while you are trying to teach the sign
Another advantage is that signing babies tend to have high self-esteems as a result of being secure in their environments.  If a child can easily communicate their needs to you then they are going to feel a sense of security.  They want something, they can tell you what they want, and you can quickly and easily fulfill his/her needs.  If a baby has no way to communicate their wants to you then it will take you longer to figure out what he/she wants which may make everyone a little frustrated in the meantime.
There are also the educational advantages that signing brings to a child as they get a little older.  Signing babies tend to have larger vocabularies once they start talking because they’ve been able to use more advanced language and are often asked more elaborate questions because their comprehension is clear to the parent.