There are many ways to encourage your little one to talk and to improve the speech of your toddler or preschooler.
Singing:
Music is used to encourage speech, create atmospheres, and improve moods. From an early age, singing and music are one of the first ways of
communication with your child. Lullabyes at sleep time, nursery rhymes at play time, musical toys for floor time.
The first songs were Hush Little Baby, Rockaby Baby, Twinkle Twinkle Little Star. Then we moved on to action songs like Speckled Frogs, 5 Little Ducks, Little Fishies, The Grand Old Duke Of York from around 4 months. I would put do the actions with her and she had a great time.
Reading:
From the moment of birth, I was reading to my baby. I read her a Winnie The Pooh Opposites book that afternoon. When questioned by the nurses, my response was "I'm giving her a head-start on language and introducing the first stages of phonics" and no more questions were asked after this. Reading books with repetitive words such as Possum in the House encourages the child's memory and can lead to the child saying the words that are repeated. In Possum In The House, a line that's repeated on almost every page is "There's a possum in the house and he's hiding in the..." and this book had her saying "House" from 6 months and the words Possum and Hiding came around her first birthday. Reading to children from a young age also introduces them to phonics and creates a relaxing environment for them to learn how to enjoy books for what they are. Books open up the imagination and by introducing them early without forcing them upon the child you are opening up a whole new world for your child to learn from and explore.
Repetitive Speech
Saying the same word over and over again will encourage your child to learn to say that word. For me, if I was giving her something or taking something away I would say "Ta" to her. If I was sitting down having communications with her I would say "Mum" or "Mumma" or "Mummum" over and over to her. If anyone ever saw her they would say "Boo" and "Hello there" so her first words were Boo, Mum, and Ta all by 7 months and Hello by her first birthday
Talking children through things
No matter what the age of your child, it's always positive to talk them through what you are doing. For instance this morning I gave mine a run-down on the weekend. That way she knows what we're doing. She's at an age now where she is talking and understanding many things and has a great memory so talking her through it is more to prepare her for the weekend than encourage speech. But with young toddlers and babies it encourages talking if they are spoken to often. You can tell a baby at 6 months what you are doing by saying "Mummy's going to put the clothes in the machine to wash them" you are not so much expecting they will know what you're on about, much less repeat the sentence, but babies are learning about communication at this age. By being spoken to, he will know that it's ok to talk to you about anything he likes. No matter how minor it is, talking to your young baby teaches him about communication. As children get older, talking through things can get them ready and emotionally prepare them for what they are doing and it tells them what you expect of them. For instance, if I tell my child we're going to be washing the all the sheets today she knows that she doesn't have to make her bed but she's to strip her bed instead. By telling her that we are going away this weekend, she knows that we will not be home and it won't be a shock to her as it would if I suddenly packed our bags and put her in the car. Good communication at this early age will set you up for better communication as your child becomes a teen and an adult. That's not to say that you can expect your teenager to actually talk to you rather than grunt! They have their own language at that age but it will improve things if you have good communications early on with your child/ren.
Using Complete Sentences and Words
This is very important when children are learning to talk. Instead of saying "Drink?" as a question, try saying "Would you like a drink of water?"
Correcting Speech
This is where I'm at right now with mine. Unfortunately due to work, she does attend childcare. Her teacher was saying "anythink" and "everythink" and "nothink" rather than using correct English. My child began using those words and I've since corrected her and she says Anything, Everything, Nothing, etc now. She had some trouble with the "R" sound and I've been correcting that, although she still says it like a "W" sound most of the time. Every time I correct her she says it properly.
Note: Once children start talking, they tend to continue talking so watch out! I know mine talked once for the entire we were travelling, which was 2 hours in the car! I'm not sure what she was on about but I know when she ran out of things to say she would recite words from a book or sing a song. So that's my warning but in the long-run it's better for them to be talking non-stop than not have the ability to talk no matter how much it drives us up the wall.
Don't get me wrong about childcare, it has its place and can also encourage a child to speak due to the amount of time they spend around children their own age.