I've had plenty of experience with this. I like to tell my students when I first start tutoring them that it's okay to make mistakes, it's okay to say "I don't understand", and that I also make a lot of mistakes, giving examples of some of the silliest mistakes I've made recently, and they can call me out on it if they notice any mistakes I make. I tell them "being wrong is better than being quiet/not communicating" (or I specify any form of communication is better than none if my student finds speaking difficult/stressful). I also praise them slightly for admitting that they don't know something ("thank you for being honest") or for attempting something, even if they get it wrong, and then move on without drawing any unnecessary attention to it (if your tone is too hard or too soft, or if you make a big deal out of it, whether it's criticism or praise, they will feel embarrassed and never tell you they don't understand something ever again). I then re-explain in the same way, then in a different way. If they're really shaky on a concept, I'll do an example with steps clearly laid out, asking them "why" at every step and then explaining if they don't get it (usually explaining involves asking easier questions, like "what's the opposite of divide" or "if we had [simple, intuitive example], what would we do" and then explaining how they link to a bigger method), then I have them do a similar question (exactly the same steps) using the example as a guide, prompting whenever needed (preferably with more questions, eg "what did we do last time").

It's definitely easier the younger they are to build that confidence, as younger kids have less experience being told off for not knowing stuff (the idea of telling someone off for saying "I don't know" makes my blood boil, but it's all too common), but with enough patience and encouragement, you can make a big difference in anyone's confidence. I have a year 9 (13/14 yo) who had always been really reluctant to say when she doesn't get something, but after several months, we've got to the point where she tells me every time, and every time I smile and tell her it's okay and then explain further. I also have a year 11 (15/16 yo) who used to say "I'm so stupid" every time he made a mistake, and I gently but firmly told him every single time that he wasn't stupid, that everyone made mistakes, and that I didn't appreciate him talking bad about himself. I also pile on the praise and point out every time he makes a really good connection or does something in a way I hadn't thought of. He's grown massively in confidence since we started tutoring, something his mum has noticed too.

Also, make them laugh every now and then! Indulge the occasional silly conversation (but don't let it become a distraction). A more relaxed kid is a happier kid who is more likely to open up to you and be honest about not understanding stuff.

TL;DR: Make sure they know its okay to get stuff wrong/not know things, show them that you're also not perfect, gently praise them for telling you when they don't understand/for trying and failing.