The single most common problem, and almost always the same cause: the browser asked once, the answer was "block", and it now remembers.
Granting access
When the interview asks, choose Allow. If no prompt appears at all, the browser has already answered for you and you need to change it.
Clearing a block
Chrome and Edge — click the icon at the left of the address bar (a camera, a lock, or sliders depending on version), set Camera and Microphone to Allow, then reload.
Safari — Safari menu → Settings for This Website → set Camera and Microphone to Allow, then reload.
Firefox — click the icon at the left of the address bar, remove the blocked permission, then reload.
You must reload after changing it. The page does not re-ask on its own.
"Device in use" or a black picture
Another application has the camera. Video call apps are the usual culprits and many keep the camera open after the window is closed. Quit them fully — not just the window — and reload.
On Windows, check Settings → Privacy → Camera and confirm your browser is allowed there too; a browser permission cannot override an operating-system one.
On macOS, System Settings → Privacy & Security → Camera, and the same for Microphone.
Inside Safe Exam Browser
If your interview runs in Safe Exam Browser the permission belongs to SEB rather than to your normal browser, and changing Chrome's settings will not help. Quit SEB and relaunch from the interview link.
Still nothing
Try a different browser before concluding the hardware is broken — it takes a minute and it separates a browser problem from a device one. If the camera works in one browser and not another, it is a permission, not a camera.