Oh, my goodness is my toddler ever a chatterbox. Thankfully, she can talk and talk and talk to herself. She does not always require a response. My kid is well ahead of the game when it comes to language development. Most people are confused about her age out in public. They think she is abnormally small for a three-and-a-half-year old, but she is two-and-a-half.
I have some background in early childhood education, and I have read twenty gazillion books on the subject, so I knew what I wanted to do to instill good language skills in my child before she was born. I'm not an expert on it by any means, but maybe you can benefit from knowing what has worked for me.
1. Talk to your baby all the freaking time
I am actually not much of a talker, so this was really awkward for me in the beginning, which is why I started practicing when my baby as barely a week old. I narrated everything I was doing ("Mommy's changing Kenna's diaper.") and everything the baby was doing ("Oh, Kenna doesn't like getting her diaper changed. Kenna is crying.").
I also held conversations with my mute baby. Ask the baby a question, leave time for the baby's response, and then say what the baby would respond if the baby were super freakish and could talk.
"Does Kenna want to wear her giraffe onesie today?" [pause]
"Oh, Kenna does want to wear her giraffe onesie. She loves her giraffe onesie."
I read something about kids not understanding pronouns until a certain point, so we always used names when talking to the baby, at least until she was using multi-word phrases.
2. Don't correct improper word usage
Once your kid does start talking, don't correct improper word usage or verb tenses. The goal is to get your kid to talk more, so you don't want to do anything that might make her feel bad, like telling her she is saying something wrong.
3. Repeat and model
When my toddler first started talking, I would repeat what she said, or what I thought she said, for two reasons. First, to make sure I understood her and, second, to model proper word usage and verb tenses.
"Jibber jabber cookie blah blah mama"
"Would you like a cookie? Oh, you do want a cookie."
"Jibber jabber cookie blah blah mama"
"Would you like a cookie? You do? Ok. Kenna said, 'May I please have a cookie, Mama?'"
I still do this but now, instead just trying to build my kid's vocabulary, it is also about using proper sentence structure. Also, I still don't know what the heck she is saying sometimes. She speaks pretty clearly, but if it is a word I've never heard her use before, I takes me a few tries to get it.
3. Don't use baby talk
This one is in every book there ever was, but there is some confusion as to what "baby talk" means. Baby talk refers to made-up words. It does not refer to using a high-pitched, sing-songy voice, which actually helps babies with comprehension and helps to calm them.
Example (not baby talk):
"Ohmygod you're so cute, I love snuggle your little neck and smoosh your cheeks and give you so many kisses." (I may have said this every single day that I was on maternity leave.)
Example (baby talk):
"Does my little shmoopykins need her dipey-wipey changed? Someone has a mess on her tushy-wushy."
You should not use baby talk mostly because you sound like an idiot when you do.
4. Have conversations with your child
This is harder when your child is a baby and you are holding both sides of the conversation yourself. It is infinitely more fun when your child can participate. This is a great parenting tip, not just for building language skills.
Have a conversation with your kid. Your entire relationship should not consist of you barking orders at your kid or even instructing your kid in a nice way. Your kid is going to need conversational skills in life and you are going to want your kid to talk to you about things as she gets older, so you might as get her used to having a normal conversation now, before she can resist.
This part is easy and it is enormously entertaining. My toddler cracks me up every single day. She is just starting to really pretend and tells me stories about monsters and her dolls and her friends at daycare.
One last note
I was talking to my hair stylist about some cute things my toddler says and she said she doesn't always understand what her nephew says, but that his mom seems to. She was worried about being able to understand her own kid when she has kids. I reassured her that she would understand her kid even if other people couldn't. It isn't like a psychic bond thing, it is just that your kid uses the word in context around you so you begin to pick up which words mean what because you are much more exposed to them than other people are.