Its a great idea! We started signing with our little one when she was about five months old and by seven months she could sign milk and more. From there it just grew. Now that she is 22 months, she is signing and talking up a storm! I looked into it extensively and babies that sign, typically have a larger spoken vocabulary when they do speak and start speaking sooner. The numbers usually indicated this to be true somewhere in the 80-95% of the time depending on the study. Its also helpful with special needs kids so more and more schools are teaching it across the board so that the special needs kids can communicate with the other kids too. This will put your child ahead of the game on this front and set him/her up for leadership opportunities most kids do not get (I am a teacher).
There are tons of books and kits about it, but the most helpful thing for us was the "My Baby Can Talk" DVD series. She was (and still is) engaged by it, and we would sit and watch with her so we learned the words too. Looking at pictures just isn't enough - it doesn't depict the movement well. Now that she is nearing two, we have also found the signing times videos helpful and she really enjoys the two that we have. She wasn't ready for them when she was younger though because they move a little faster.
In addition, there is a website called aslpro (www.aslpro.com) that has court translators signing a whole bunch of signs and you can alphabetically look up any signs of interest to you on there as well. This is a great resource for when you are finding you are using a word over and over again and would like to know the sign for it but the word isn't on the videos. It doesn't have everything, but it does have quite a bit.
My husband and I found that it wasn't too hard to learn one word/week - or more because many of the signs just make a lot of sense any way. We started out with five words and then added from there. I had already learned the alphabet which helps because it makes it easier to understand a lot of the hand shapes that are used. But it will be awhile before you would want to know it with your little one any way so if you learn one word and 5 or 6 letters a week you'll be up and running in no time!
I do not recommend the Baby Einstein signing videos until after your baby is at least one and a half, not because they are bad, but because the signs they choose are less useful (window, refrigerator etc.) than many others and even the signs given like the one for blocks tend to be long with a lot of steps. In sign, there are many words that have less, specific, short versions for example, the sign for chicken is usually signed just as the word for bird, but if you want to be detailed there is a more detailed sign (that involves more steps) for chicken. Blocks and Puzzles are two words like this and the baby einstein series gives you the long, detailed version with is harder for babies to put together. Now that she is older we have watched it some, it does engage her and she thinks the puppet shows in between are funny. She usually signs part of the signs given that are more involved and we get the idea.
I have actually met a couple of deaf people now and am looking into learning to be an interpreter - maybe - tough job. But they are always more than happy to help by giving advice on resources when I need it. You may find the same thing happens to you! I met one in the pediatrician's office when she saw my baby and I signing the colors together.
Good Luck and Let me know if you need any additional information or advice, or resources!
Make sure to post us all on how it goes too!