To install the Mosquitto broker, first update your package list using 'sudo apt update'. This ensures your system knows the latest software versions. Next, install Mosquitto with 'sudo apt install -y mosquitto'. After installation, start the Mosquitto service using 'sudo systemctl start mosquitto'. To make sure Mosquitto starts automatically after a reboot, enable it with 'sudo systemctl enable mosquitto'. Finally, verify the service is running by checking its status with 'sudo systemctl status mosquitto'. When all these steps complete successfully, your Mosquitto broker is installed and ready to use.