Singing: Songs teach so many language skills: vocabulary, syllables, rhythm and rhyme.
You can sing ANYTHING - whatever you love from the radio, songs that were sung to you when you were little, your schedule of the day (I am very guilty of singing songs to my kids about getting dressed, feeding time, bed time etc.). The next time you are in the car, sing along to whatever you are listening to. When you are out on a walk, sing about the trees and cars you are passing by (or you can just point them out and make conversation with your little one). My favorite songs to my first child were the ones from his toys that played music. They were so catchy and they were Fisher-Price's versions of songs about the colors, the parts of the body and some bizarre "I Love You" song that has become a staple in my household.
Rhyme Time:
Nursery Rhymes, "Action" rhymes and Bouncing rhymes are different ways of engaging your child when they are just on your lap hanging out. Rhymes like "Pat-A-Cake" or "Hickory-Dickory-Dock" are great because your baby will follow your hand motions and eventually will do it himself. It's very exciting when that happens!!
As a baby gift someone bought me an "Old MacDonald Had A Farm" hand puppet that had five different farm animals on each finger. I would use it every time I sang that song to my babies and they became my child's "friends". Puppets are a great tool to singing rhymes, and you can make them yourself pretty easily. "Action Rhymes" include the songs you use your hands for, Itsy Bitsy Spider, Open, Shut Them, Mr. Sun etc. Babies love to be tickled and this is a great way to bring on the giggles!
My personal favorites are action rhymes with a bounce - I find they excite babies most of all. Some of my go-to's are 1,2,3 OOPS! (bounce your baby 3 times and then open your legs so they "fall") it is a guaranteed pleaser, The Grand Old Duke Of York and Father and Mother and Uncle John. You can always Google songs and rhymes for ideas if you get stuck, or just turn on any music device and dance baby dance! These are actually great because they teach your children literacy skills while also moving around - win win all around!