It just so happens that I went to the library and printed out mine just yesterday. It’s a more-or-less official-looking certificate with all the relevant information in readable plain-text plus a huge QR code. There’s a web site you can go to for it.
For any vaxed California people who haven’t seen this yet, the site is:
Digital COVID-19 Vaccine Record
Enter some basic information to sign up. It will send you a link, that you can receive either via a text message or an e-mail. Then click on that link to view your certificate.
ETA: You also have to choose a 4-digit PIN code. I don’t know if the person who’s verifying your vax, upon scanning your QR code, also has to enter this PIN code to see if. I suspect not. If so, then he should probably hand his smart-phone to you to enter the code. Anyway, it might be important for you to have your PIN code handy. I haven’t had occasion to try this yet.