Docker container permission management involves user permissions and container capabilities. By default, containers run as the root user, which poses security risks. Best practices: 1) use the USER instruction in Dockerfile to switch to a non-root user; 2) use the --user parameter to specify the running user; 3) use --cap-drop to remove unnecessary Linux capabilities; 4) use --cap-add to only add necessary capabilities; 5) use the --read-only flag to make the container file system read-only; 6) use --security-opt no-new-privileges to prevent privilege escalation; 7) use AppArmor or SELinux profiles for enhanced security. For operations requiring root privileges, use sudo or capabilities for fine-grained control.