There are a lot of good resources on the internet for you on how to talk to kids about climate, and age-appropriate resources for them too, like NASA's Climate Kids.
We've distilled the 'how-to-talk-to' recommendations into four:
1) Be Self Aware. Odds are, if you are reading this page, you have your own anxieties about climate change, and it's important to examine those beforehand. As parents, we don't want to project our fears onto our kids. We can acknowledge that we may be scared too, but our job here is to support them, not have them share our burden.
2) Teach Nature. Before you get into the specifics of climate change, you can take every opportunity to experience nature with your kids and to cultivate their curiosity. Go outside together, dig in the dirt, watch critters, and establish a connection with the Earth in your backyard. Talk about systems - how that houseplant on the windowsill makes oxygen, where your water comes from and goes, where your food comes from. This foundation will prepare your kids for what's next.
3) Tell The Truth - At Their Pace. You know your child and know when they are ready for things. Younger kids don't need to know how serious things are, but older kids will begin to hear things on the news and in school. Check in with them and answer questions they have honestly. if you don't know the answers, offer to learn together. Again, acknowledge that this can be scary, but convey that humans have come together many times throughout history to solve big problems together.
4) Give Them Agency. Help your kids engage in solutions. This can be around the house changing personal habits - eating less meat or biking rather than driving for short trips - or it can be getting your kids involved in school or in the community in nature or recycling programs or even in advocacy if they are inspired by youth like Greta Thunberg. When kids feel like they are doing something about the problem, they will feel less anxious.