We taught Princess Sparkley a few signs as a baby because my sister had taught her little girl who was older and it was cute. It's helpful for the baby to have a way to communicate before they can speak. We taught PS a bunch of signs, but the main ones were: please, more, all done, all gone and milk. She learned them because she was a baby prodigy, but for the most part, she was able to speak as soon as she was able to learn the signs so it wasn't really needed.
Buddy didn't really do much aside from the occassional "words" and a lot of grunting until he was two. Signs were great for him. One of my favorite videos of him is when he's about 14 months old standing at the fridge frantically signing "please" (rubbing your hand on your chest) because he knew the blueberries were in there.
Knowing how well sign language worked for Buddy, and since we were planning on using it with all of our kids a little bit, even before we decided Baby X had delayed speech as well, we started trying to teach Baby X signs. He wouldn't learn them. He's been really quick at things like rolling over, sitting up, crawling, standing, walking, but smaller motor skills like waving and clapping, he was slow on. He just barely started waving regularly a month ago. So we've been super excited this week and last as he's finally started to sign to us. He knows please (rubbing your hand on your chest), more (knocking your pinching fingers together), all done (raising hands in the air like the call for touchdown-- although I don't think this is technically ASL) and, unrelated, he'll finally point to his nose when I ask him where his nose is. Hooray!
these videos. Even my two older kids really enjoy them. Buddy, especially comes running if he hears the theme song. The videos mix sign language with music and songs. For those of you in the loop as far as LDS things go, Rachel Coleman, who started these videos with her sister, is LDS and the daughter of Lex de Azevedo who has done a lot in church music for EFY and such, I believe.* In the behind the scenes part of the dvd, she talks about how sign language can be effective for any child, not just a deaf child because it enables them to communicate before they can talk preventing tantrums and fits. Even with Baby X he grunts and grunts with these long stories and I can tell he's frustrated that he can't just tell us.
You can check out some of the videos here.
These board books are great. We have four of them: My First Baby Signs, Baby Signs for Mealtime, Baby Signs for Animals and Baby Signs for Bedtime.
Sign with your Baby by Joseph Garcia
I use this book mainly for its glossary of signs in the back.
*Plus, for a personal connection, the two kids in the video are Leah, Rachel's deaf daughter, and Alex, her hearing nephew. Alex's dad grew up with my sister and sister-in-law and when Jed and I were first married, we were in Alex's grandparents' ward. My kids think this is awesome.