The Depot CLI uses your local Docker credentials provider. To allow your Depot build to access a private image registry, log into the registry with docker login registry.example.com on the same machine where you'll run depot build. Use the private registry in your Dockerfile as you normally would:
FROM my-private-registry/project/image:version
# rest of your DockerfileThen run depot build ..
You should be able to use any registry with no additional Depot configuration. If you're having issues accessing private registries from your builds, see Cannot pull from private registry during build.