Talk less, listen more.
What we see as sharing some choice pearls of wisdom on our part, can quickly turn into momsplaining or dadsplaining on theirs. If you want to get your kids to talk more, you have to talk less, that's just how it works.
Even better than talking less...learn to ask questions. Not just any questions...curious, open-ended questions are best. We ask questions like, "How was your day?" which invites one-word answers like "okay" or "good". Instead, try asking something more curious and inviting such as, "What was the best/worst part of your day?" or "What was one thing you learned today?" or even "What was something funny that happened today?"
I can already feel your nerves and objections..."this will never work with my kid", you're thinking. Well, just like learning to ask good questions will take you some practice, your kids are going to need to adjust to being the one taking up the space and doing the talking. Be patient with this, remember that Rome wasn't built in a day. Just practice asking those open-ended questions (here's a tip - they usually start with the word "What") and then WAIT. Give them a chance to think about your question, and be willing to wait for their answer. If they give you an "I don't know" then ask a different question. Or ask, "What should I ask you about your day?" (See, that question started with the word "what").
What to do when you miraculously DO get more than one word out of your child: 1) Get really excited (on the inside only please) that your kid trusts you enough to share any small tidbit of their personal life with you. 2) Ask another question. Whatever you do...do NOT use this as a chance to jump in and revert back to doing all the talking. No matter what you feel about their answer, keep that to yourself and ask another question. Eventually, you'll have them sharing volumes with you and you'll wonder if you've created a monster, but it's okay. They are pretty loveable monsters.
Whatever you do...don't give up! If you, like most parents I talk to, are dying to know more about the inner world of your kids, this is the doorway inside. The more your kid trusts that you're going to make space for them to share, the more they will invite you in.