It uses a standard protocol (CTAP2 - https://fidoalliance.org/specs/fido-v2.0-rd-20170927/fido-cl...) that's part of the standards for FIDO2. IIRC as long as your OS lets your application speak to the YubiKey over USB, you should be able to use this in the application. In the browser, you can just use WebAuthn.
If you want to see how a native app can talk to the YubiKey, you can play with Yubico's own implementation: https://github.com/Yubico/python-fido2/
For browser based code, you can use WebAuthn and leave the device communication to the browser and OS: https://developer.mozilla.org/en-US/docs/Web/API/Web_Authent...